Here is the full list of all 11 Abyss Crew achievements.
Seat on the pilot station
Seat on the sonar station
Seat on the gunner station
Seat on the engineer station
Play as Abyss Master
Destroy Moby Squid
Destroy Red Octopus
Destroy Apocalypse Jaw
Embark aboard Turtle Submarine
Embark aboard Oyster Submarine
Embark aboard Guppy Submarine