KIEV, Ukraine—“Hello. I’m your killer,” Oleksiy Tsymbalyuk said when he met Arkady Babchenko, a Russian dissident journalist, for the first time this spring.

The next time the two men saw each other, in late May, Mr. Babchenko was lying in a pool of pig’s blood inside his Kiev apartment, which had been meticulously prepared to look like the setting for an assassin’s hit.

“Good...