Here is the full list of all 10 The TakeOver achievements.
Complete the story playing as Jackson.
Don't lose a life in a single play through.
Beat 100 enemies in survival mode.
Shoot down 500 enemy aircraft in survival mode.
Get both game endings.
Complete the story.
Complete the story in relay mode.
Complete the story in co-op mode.
Complete the story in hard mode.
Beat the final boss without getting hit.