Max Payne. Maximum pain. Never has a video game character been stuck with such an autobiographical name. We were, after all, introduced to this archetypical tough New York cop just as drug addicts slaughtered his wife and baby.

In the game's sequel, sadistically subtitled The Fall of Max Payne, he forms a spiky relationship with assassin Mona Sax, only to see her gunned to death by a Russian mobster at the downbeat finale. Even for a tough New York cop, that's got to hurt.

Fast-forward eight years and things aren't getting any rosier. Max is unemployed and living in a dingy apartment in Hoboken, New Jersey. He's washed up, washed out, addicted to painkillers and propping up bars like some reject from a Bukowski poem.

With a pitiless eye for detail, the art team at Rockstar Vancouver has crafted a nightmarish bachelor hovel for the character, all empty takeaway packets, peeling wallpaper, busted furniture and god-knows-what staining the carpets and mattresses.

Then on a snowy night in New York, Payne bumps into an old colleague, Raul Passos. Raul tells him there is lucrative security work available in South America; he says there's a job Max is perfect for. "What, you can get me work sitting in a bar all day feeling sorry for myself?" Max growls in that distinctive monotone. "Where do I sign up?"

But Payne needs an escape route – he's just killed the psychotic son of a notorious mob boss, Anthony DeMarco, and pa is out for revenge. Back at the wretched flat, Passos is selling the job to Payne, when DeMarco and his mob turn up for a shoot-out.

And we're into the action. "This game is all about the mechanics," explains Rockstar's VP of development, Jeronimo Barrera. "We wanted it to be the most fully-realised third-person shooter ever made; it needed to have the craziest physics, the most accurate and responsive controls. It had to be visually stunning. Running around shooting people is essentially what you do in this game – but it had to be the most fun you've ever had running around shooting people."

As Payne bolts through the rotten corridors of his decomposing building, bullets smash through windows and heavies can be heard clambering upstairs, shouting insults. Although the Rockstar spokesperson showing me the game stresses that this is not a cover shooter, there is an "intelligent" cover mechanic – on the Xbox 360, hitting X makes Max stick to any nearby wall or object suitable for protection. From here, he can spray bullets in any direction, angling his gun around or over the obstacle.

There is environmental damage, too. As Max fires back, the window frames shatter; objects smash and fall. It's a detailed, intricate world.

It's also typical Rockstar.

Just as Max appears to be cornered at one point, a mad-eyed Vietnam vet bursts out of a nearby apartment with a shotgun, blasting down a couple of mobsters, and shouting: "Come to me you sinners, you evil men – you will be cleansed in fire!"

Later, we can sidetrack into his apartment, which is stuffed with bomb-making equipment, the walls covered in scrawled messages. It's the sort of surreal interlude that harks back to the previous Payne titles, but is also heavy with the movie references we know from GTA and Red Dead.

Max Payne 3

So Payne escapes and heads down to the vast Brazilian metropolis of São Paulo ("You've been kicked out of the force … and you've killed a lot of people," says Barrera by way of explanation). There he takes on a job protecting wealthy real estate magnate Rodrigo Branco, whose trophy girlfriend has been kidnapped by a street gang. Naturally, they want a suitcase full of cash for her safe return and Payne is going to be the transfer man.

This all takes place in a nervy, exciting sequence in a huge football stadium. The drop is due to be made on the pitch, but things go awry when a paramilitary group turns up and starts blasting at everyone else. Cue a desperate series of chases and shoot-outs as Max and Raul race through the labyrinthine complex, looking for the gang member with the cash.

We also witness one of the game's many interactive cinematic experiences, where the speed slows down and Payne gets to attempt a ridiculously showy stunt. In this case, he gets onto a gantry above the stadium's press box where a sniper is looking to take out Raul. Max grabs a rope and swings down into the chamber, shooting his way through the glass screen and into the face of the would-be assassin. Game over.

It's a function designed to empower the player and capture that sense of invulnerability inherent in the great action movie characters. Players will find that during these sequences, their ammo will top up and they'll be harder to injure. It's about not just capturing the obvious tropes of action cinema – the visuals, the gunplay, the choreography – but also the underlying narrative systems. The cheats.

There's another similar feature named Last Man Standing, which comes in to play if you're fatally wounded – on the way to the ground, you'll get one final chance to shoot the enemy, via a shaky reticule. Take him out, and the game will instantly employ any unused painkillers you're carrying to boost your health and revive you.

Also in the spirit of the classic Hong Kong action movies, Payne is never far away from a discarded gun; all of which can be picked up and wielded. The weapon wheel system will be familiar to any Red Dead Redemption veterans. To access an item, you hit the button to bring up the wheel and cycle through Payne's available armoury. He can carry two single-handed weapons, dual-wielding them if he chooses – he'll happily leg it around with a Beretta in one hand, an Uzi in the other. He can also carry one rifle or carbine.

Of course, the defining weapon in the Max Payne armoury has always been bullet time. Initially inspired by the bullet ballets of John Woo and Ringo Lam, it allows players to trigger a slow-mo action sequence in which multiple enemies can be targeted and shot without fear of recourse. There's a lock-on system in place, but players can choose to free aim their way through these encounters. However you go, it remains a gameplay concept of skewed genius, simultaneously boosting the player's abilities and providing moments of breathtaking cinematic clout.

In Max Payne 3, the system functions in the same old way – access to bullet time relies on a dedicated power gauge, which is filled during shoot-outs. But of course, what's new is the impressive graphical fidelity, and the sheer fluidity of the movement.

Rockstar has employed NaturalMotion's Euphoria physics-based animation system – every leap, roll or fall is procedurally driven, based on a richly detailed 3D character model, susceptible and reactive to all the forces of velocity and impact. The physics system also comes into play via the contextual bullet contact, which ensures that leg, arm, body and headshots all lead to very different reactions. Enemies never go down the same way twice.

Furthermore, the animation has none of that floppy "rag doll" feel that cursed early experiments in physics-based movement. During the stadium sequence, we see Max leap across corridors and crunch into walls, bracing himself for impact at the close of the dive. He'll also chuck himself backwards over low walls, landing with sickening solidity on his back, guns firing between his legs.

Cleverly, however he lands, you retain multi-direction control over shooting. If he leaps across a room and lands on his back, you can stay prone, turning and blasting in all directions, before getting back on to your feet. It gives the game a sense of physical fluidity and adaptability, which also heightens the cinematic feel. Midway's Strangehold got close to bringing us the athleticism of the Hong Kong action flick, but Max Payne 3 ramps up the sheer physicality.

Max Payne 3

Next, Rockstar shows me a sequence that takes place later in the game, but still before Max transforms into the bald-headed, hulked-up figure we've seen in the screenshots and trailers. He's at an old bus depot, looking after Raul's girlfriend Giovanna, when that pesky paramilitary group turns up again. There are shoot-outs in an old bus cemetery, where the rusting skeletons of ancient vehicles provide the only cover. Yep, it's an escort mission, but Giovanna will generally run and hide, taking care of herself, while you engage the masses of black-clothed soldiers.

Inside a bus repair garage, Payne climbs the scaffolding to an upper level, and we get another slow-mo sequence. This time, he grabs hold of a rope that's running to the floor level and slides down it, taking out enemies en route. There are, it seems, plentiful nods to Die Hard as well as the likes of Killer and Hardboiled.

Next, Max bursts his way into an office area and, during our shotgun shoot-out, blasts an enemy though a window, showcasing the animation and environmental destruction in one gloriously OTT second. Each shoot-out ends with a bullet-cam moment, as we follow the projectile from chamber to final enemy, the impact complete with a requisite spray of claret. It's gruesome stuff, but guiltily satisfying.

This section shows how Max Payne 3 will transition between scenes using a new variant on the comic books frames that told the ongoing story in the first two titles. Now. We'll see 24-style animated story sequences – or "motion comics" shot from multiple views, as we're taken between narrative chapters and locations.

Shoot-out sequences are also intercut with story and dialogue moments, though Rockstar has been keen to keep the flow between mo-capped plot sequences and the physics-based animation of the game as smooth as possible. Indeed, the mo-cap sequences with Max actor James McCaffrey and the rest of the cast were all filmed at Rockstar's own studio in Brooklyn.

The team apparently built elaborate sets to replicate game maps, allowing the actors to interact much more naturally with their environment, and allowing closer parity with the in-game action. Plus, every non-interactive story section will feature Max carrying the weapons that you're actually holding in the game at the time; it'll also show any scars or blood stains that he's picked up during play – a small point, but a cool one in terms of continuity.

Our demo ends with Max and Giovanna bolting into a bus, with paramilitary goons in hot pursuit, one of them wielding a grenade launcher. Giovanna gets behind the wheel and decks the accelerator as Payne shoots out a nearby fuel depot and AI enemies scatter. Panicking, she drives the bus straight into a brick wall. Another fine mess for Mr Payne.

Elsewhere, Rockstar has revealed a major multiplayer component to the game. The range of 16-player modes are all designed to capture the campaign's cinematic intensity and emphasis on acrobatic gunplay. Alongside standard deathmatch and team deathmatch options the key draw is likely to be the innovative 'Gang Wars' newcomer, which, like the multiplayer in Uncharted and Assassin's Creed, brings a narrative slant to the action.

Built around set-piece locations from the campaign (with previously inaccessible areas like rooftops, now opened up), teams compete to achieve a series of objectives, all accompanied by Max Payne's usual gruff monologue and book-ended by the graphic novel cut-scenes.

Somehow, Rockstar has managed to incorporate bullet-time into the action. When a player triggers it, everyone in their sight line is caught in the slow-mo treacle, making for bunch of easy, rapid kills. There's also a range of new special abilities known as bursts, which become available when the player fills an adrenaline gauge.

Killing enemies and looting their bodies builds the meter, and each burst power has three levels of power. Participants can loot the bodies of fallen enemies to find ammo and painkillers. XP is earned though kills and assists unlocking new weapons and bursts. It's also possible to start a vendetta against any player that kills you twice – get them back and you earn bonus XP.

It sounds like an interesting concept, and married with the visceral combat and dark narrative of the single-player, suggests we're in for the first essential shooter of 2012. Whether Rockstar can work its peculiar magic on such a linear experience is the main question.

Max Payne 3

Players can briefly explore certain areas of each location, but this is a narrative ride, with no open-world freedom. Remedy, the original developer of the first two titles is no longer involved – now a group of Rockstar Studios, including Vancouver, the creator of school-based adventure Bully, are at the helm.

There is a realisation that this is a significant undertaking. "Max Payne invented a lot of the vocabulary of the third-person shooter," says Barrera. "It was one of the first to really tell a story through the action."

Yet, on the flip side, the linearity has allowed Rockstar Studios to absolutely cram each locale with scene-setting detail. San Paulo, from its mansions to its slums, has been rendered with a real eye for the diversity of the place; members of the design team went out there for six weeks, soaking up the atmosphere, the music, the culture and photographing everything.

There's mass poverty, but also great wealth (Barrera delights in telling me this place has more helicopters per capita than any other city on Earth), and apparently, you'll meet resistance from all areas of society during the game, battling both highly trained military squads and favela gangs – all with their own AI behaviours.

The story of Payne's quest for redemption looks to be a classic action thriller arc – the stuff of Brian de Palma or Tony Scott (Man on Fire is apparently a favourite movie with the Houser brothers). And at some point in this story, as in all wayward action flicks, the anti-hero realises he's got to stop running and face whatever's coming for him.

That's when the clippers come out and the new Max emerges. We can expect all hell to break loose – it's what Rockstar always promises and usually delivers. One way or another, the pain is going away.

• Max Payne 3 is due out in March 2012 on PC, PS3 and Xbox 360