"While using the Slug Cruiser, kill 3 enemy crew members with one shot from the Anti-Bio Beam."
To earn the Disintegration Ray achievement, a bug in the game can be exploited where a player teleporting their own crew members on to the enemy ship during a battle can then kill those crew members with a shot from the Anti-Bio Beam and they will be included in the total killed (along with any enemy crew).
Killing System Repair Drones or Anti-Personnel Drones also counts to the limit of enemy crew members killed.
An easy way of aquiring this achievement is to find either a Rebel Rigger or Mantis Scout (which can be found as early as the first sector), both of which spawn with at least three crew members, usually lined up nicely for the Anti-Bio Beam. It is also recommended to attack an empty room to lower the shields, as damaging a system can cause the crew to move around.