Psi Reavers are an interesting enemy, as, rather than being truly flesh and blood, are in fact the psionic projections of a Psi Reaver Brain that you'll find nearby. As such, attacking the Psi Reaver itself will only cause it to temporarily disappear until the Brain is destroyed. Psi Reavers have a powerful ranged attack, but it is fairly easy to dodge. Your first Psi Reaver will be found at the end of Command deck; unlike most other enemies, Psi Reavers do not respawn or appear randomly; instead they only show up in a few fixed locations.
A second version of the Psi Reaver, the Greater Psi Reaver, also exists, though it only shows up once. Please see its own page for details.
Attributes: Very high Hit Points, high damage, medium attack speed, slow movement speed
Weaknesses: Anti-personnel ammo, incendiary damage
Common Loot: Psi Reaver Organ
Strategy: The Psi Reaver is a bit different from other enemies. Rather than attack it directly, you should instead search for the Brain that powers it, which will usually be hidden nearby, somewhere in either the same or an adjoining room. The Psi Reaver itself is big, tough and does a decent amount of damage, so it's generally not worth attacking directly. Once the Brain has been destroyed, the Reaver itself can be killed for good.