Here is the full list of all 11 Tiamat X achievements.
Completed the game without losing a single life
Level 6 completed
Completed the game
Level 5 completed
Completed a level firing only the minimum amount of shots to get the job done
Level 4 completed
Level 3 completed
Completed a level without losing a life
Level 2 completed
Killed all enemies on a level
Level 1 completed