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