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Part of the difficulty in studying time perception is that memory is known to be biased by numerous factors including arousal and salience. So while people commonly report time slowing down during specific events, it is difficult to differentiate the effects of retroactive memory bias in encoding and recall from actual increased resolution in the perception of time and accelerated physical abilities or mental processes. For example, adrenaline is known to affect both physical response and memory consolidation.

One hint regarding the plasticity of the brain's actual perception of time comes from the temporal binding effect (nice review here). A variety of experiments show that the brain automatically recalibrates simultaneity amongst different neural processes through learning: That is, the brain processes different stimuli at different rates, but it learns to calibrate those processes so as to create the illusion that they occur at the same time:

At least over a short time frame, our temporal perception of events is far from veridical, and multiple timelines are capable of dynamic recalibration.

In other words, there is no single perception of time, time is perceived at different rates by different parts of the brain, and then retroactively synchronized.

A more direct attempt to differentiate memory from perception was done by Stetson et al (2007). In this experiment, subjects were dropped 150 feet with no ropes or parachute - into a safety net. During the free-fall, they were asked to read numbers flashed on a wrist-watch. The numbers were flashed at different rates to test whether perception resolution was actually enhanced during the fall. Despite estimating their fall to take much longer than control subjects not performing this task (corroborating the effect of salience on memory), there was no evidence of increased time resolution:

Our findings suggest that time-slowing is a function of recollection, not perception: a richer encoding of memory may cause a salient event to appear, retrospectively, as though it lasted longer.

However, this conclusion has been criticized by other authors as the failure to produce an effect on time perception may be due to the experiment not being frightening enough, for only testing visual perception, and that free-fall may actually distract from the reading task. Evidence from life-threatening events such as accidents and the performance of skilled individuals in extreme sports for example, suggests that increased time resolution, physical performance, and cognitive abilities during extremely stressful events may be possible:

This evidence supports the suggestion by Arstila (2012) that humans possess a specialized hormonal or neurophysiological mechanism for high-speed cognition; and that this is activated inadvertently by real fear of imminent violent death in accidents, emergencies, and certain extreme sports; and may on some occasions be activated intentionally by individuals who have trained themselves to do so.

Edit (re updated question):

The latter paper - Buckley (2014) - summarizes research on the performance of experienced / trained / skilled individuals. Accelerated performance (physical and mental) is found in accidents in extreme sports, such as climbers in accidental falls; and in the performance of many physical activities: