Here is the full list of all 16 Dual Core achievements.
Corby joined your team!
You tried Story Mode
You completed story mode with 'Normal' difficulty
You completed Story Mode with 'Hard' difficulty - impressive!
You completed Story Mode with 'Expert' Difficulty. Wait? What? How is this possible?
You completed Arcade level 1 - nice work!
You completed Arcade level 2 - no small accomplishment!
You completed Arcade level 3 - Impressive!
You completed Arcade level 4 - this was supposed to be virtually impossible - apparently it's not!
You doubled the fun by playing with a friend!
You played with 2 friends - hope you shared the health pickups...
Congratulations, you played 4 player mode for maximum multiplayer mayhem(TM)
You played versus mode with 3 bots, on Normal difficulty, and won!
You played versus mode with 3 bots, on Hard difficulty, and won!
You played versus mode with 3 bots, on Expert difficulty, and won!
Triple Pink! You maxed out your laser upgrades!