Boss Rush mode - Successfully complete Xbox 360 mode to unlock Boss Rush mode.
Extra credits - Successfully complete levels to unlock additional credits.
Free Play mode - Successfully complete Level 2-7 to unlock Free Play mode.

Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Defeat Boss in Level 1-1 (10 points): Try and defeat Boss in Level 1-1 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-2 (10 points): Try and defeat Boss in Level 1-2 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-3 (10 points): Try and defeat Boss in Level 1-3 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-4 (10 points): Try and defeat Boss in Level 1-4 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-5 (15 points): Try and defeat Boss in Level 1-5 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-6 (15 points): Try and defeat Boss in Level 1-6 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 1-7 (15 points): Try and defeat Boss in Level 1-7 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-1 (20 points): Try and defeat Boss in Level 2-1 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-2 (20 points): Try and defeat Boss in Level 2-2 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-3 (20 points): Try and defeat Boss in Level 2-3 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-4 (20 points): Try and defeat Boss in Level 2-4 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-5 (30 points): Try and defeat Boss in Level 2-5 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat Boss in Level 2-6 (30 points): Try and defeat Boss in Level 2-6 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Defeat True Boss in Level 2-7 (30 points): Try and defeat True Boss in Level 2-7 (Xbox 360 Mode/higher than Normal/Dual unavailable).
Title Achieve "HERO" (40 points): Try and clear on one credit in Hard difficulty (Xbox 360 Mode/Dual unavailable).
Mission 1 "Fairy Rescue" (5 points): Rescue of the Fairy (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 2 "Pre-emptive Strike" (10 points): Clear LV.2 at a Flash Shot rate over 4.25 (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 3 "Jeep Destruction" (10 points): Destroy the Jeep (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 4 "1UP Acquisition" (10 points): Acquire 1 More Item (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 5 "Tank! Tank! Tank!" (10 points): Destroy the Entire Tank Regiment in LV.5 (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 6 "Annihilate the Fleet" (15 points): Destroy the entire Hostile Fleet in LV.6 (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
Mission 7 "Total Destruction" (20 points): Destroy 100% of enemies in LV.7 to clear (Xbox 360, Score Attack/higher than Easy/Dual unavailable).
5,000,000 points (5 points): Aim for 5,000,000 points (All game modes/difficulty not applicable/Dual unavailable).
10,000,000 points (5 points): Aim for 10,000,000 points (All game modes/difficulty not applicable/Dual unavailable).
20,000,000 points (5 points): Aim for 20,000,000 points (All game modes/difficulty not applicable/Dual unavailable).
Gallery Complete (5 points): Collect the gallery data of all the ships.
Vulcan Fighter (30 points): Clear by using the Vulcan only (Xbox 360 Mode/Continue OK/higher than Easy/Dual unavailable).
Laser Specialist (30 points): Clear by using the Laser only (Xbox 360 Mode/Continue OK/higher than Easy/Dual unavailable).
Plasma Craftsman (30 points): Clear by using the Plasmalaser only (Xbox 360 Mode/Continue OK/higher than Easy/Dual unavailable).
The Proton Magician (30 points): Clear by using the Protonlaser only (Xbox 360 Mode/Continue OK/higher than Easy/Dual unavailable).
Title Achieve "ACE" (35 points): Try and clear on one credit in Normal difficulty (Xbox 360 Mode/Dual unavailable).
Title Achieve "LEGEND" (45 points): Try and clear on one credit in Very Hard difficulty (Xbox 360 Mode/Dual unavailable).
Title Achieve "INCREDIBLE" (50 points): Try and clear on one credit in Ultimate difficulty (Xbox 360 Mode/Dual unavailable).
"The Breakthrough" (10 points): Clear Level 1 in Double Play (Xbox 360 Mode/higher than Normal).
"One in Body and Mind" (30 points): Clear Level 3 in Double Play (Xbox 360 Mode/higher than Normal).
"Full Proficiency" (50 points): Clear 1 round in Double Play (Xbox 360 Mode/higher than Normal).
Clear ARCADE (30 points): Clear Arcade Mode (Continue OK/higher than Normal/Dual unavailable).
Clear 1 Round (35 points): Clear 1 Round of Arcade Mode (Continue OK/higher than Normal/Dual unavailable).
Clear 2 Rounds (40 points): Clear 2 Rounds of Arcade Mode (Continue OK/higher than Normal/Dual unavailable).
Clear BOSS RUSH Mode (30 points): Clear BOSS RUSH Mode (Continue unavailable/higher than Normal/Dual unavailable).
Sol Destruction (30 points): Destroy all Sols in Level 1 - Level 7 (Xbox 360, Score Attack/Dual unavailable).

Additionally, there are six secret achievements:

Secret achievement (20 points): Unknown.
Bombs Away (5 points): Used a bomb and destroyed 12 or more enemy characters at once (All game modes/Dual unavailable).
Not A Scratch (15 points): Cleared the LEVEL with no extra ships or bombs (All game modes/Dual unavailable).
Implosion (15 points): Forced the boss to blow-up by itself before time was up (All game modes/Dual unavailable).
Fire Flower Festival (15 points): Used all 7 bombs in stock. (All game modes/Dual unavailable).
Secret achievement (30 points): Unknown.