Assassination targets are near-immortal. They do not take damage from normal attacks/gunfire.
They do, however, take damage from status procs, such as Slash and Toxin.
Void Dashing through the target will hurl them in the direction you dash in, and hurling them into the water will kill them instantly.
Assassination stages are targeted at a specific Corpus base, and at least one player must remain in that base during the credit collection and assassination stage