Here is the full list of all 12 Ikaruga achievements worth 200 gamerscore. It takes around 15-20 hours to unlock all of the achievements on Xbox 360.
Destroy Eboshidori!
Destroy Buppousou!
Destroy Uzura!
Destroy Misago!
Destroy Tageri!
Complete Chapter 1 in any mode with a grade of A or better
Complete Chapter 2 in any mode with a grade of A or better
Complete Chapter 3 in any mode with a grade of A or better
Complete Chapter 4 in any mode with a grade of A or better
Complete the Final Chapter in any mode with a grade of A or better
Clear the game in any mode without using Continue
Clear a certain chapter in any mode without shooting at all