Here is the full list of all 24 Crisis Wing achievements.
Fully power up a weapon
Lose a life during a secret bonus wave
Destroy 200 medium or large enemies with the green sub-weapon equipped
Destroy 1000 small enemies with the red sub-weapon equipped
Destroy 50 Bosses or Mid-bosses with the blue sub-weapon equipped
Have at least five (5) bombs at once
Have at least five (5) lives at once
Defeat the first boss
Defeat the third boss
Reach the sixth stage
Reach the last stage
Defeat the giant cruiser in the last stage
Defeat the last boss
Get at least one million (1,000,000) points
Catch a 10,000-point medal
Finish the time attack mode before the timer runs out
Score at least 300,000 points in the time attack mode
Score at least 300,000 points in the boss rush mode
Complete the boss rush mode
Destroy 10,000 enemies
Destroy all destructable parts from a boss or midboss
Find a secret bonus wave from a level
Complete all seven stages in either One or Two Player Game mode without using a continue
Complete a stage in one of the subsequent game loops