Here is the full list of all 47 Spartaga achievements.
Lose 25 games.
Complete 3 stages without losing a ship.
Complete 10 stages without losing a ship.
Complete all stages without losing a ship.
Reach 100 kills in marathon mode.
Reach 500 kills in marathon mode.
Reach 1500 kills in marathon mode.
Kill 200 ships total.
Kill 1000 ships total.
Kill 5000 ships total.
Kill Boss 8.
Kill Boss 16.
Kill Boss 24.
Kill Boss 32.
Kill 1 Dummy.
Kill 100 Kamikazes.
Kill 100 Butterflies.
Kill 100 Shooters.
Kill 100 Moles.
Kill 100 Rainys.
Kill 20 ships with a single use of Smash.
Kill 10 ships while within a single use of Slowmo.
Kill 24 ships with a single use of Blast Missile.
Keep Megalaser going for 10 seconds.
Keep Megalaser going for 60 seconds.
Complete 1 stage in Pacifism mode.
Complete 10 stages in Pacifism mode.
Complete all stages in Pacifism mode.
Complete 1 stage in Speedy mode.
Complete 10 stages in Speedy mode.
Complete all stages in Speedy mode.
Complete 1 stage in Elite mode.
Complete 10 stages in Elite mode.
Complete all stages in Elite mode.
Kill 100 Bouncers.
Kill 100 Chasers.
Kill 100 Exploders.
Kill 100 Frogs.
Kill 100 Mr. Beams.
Kill 100 Pulsars.
Kill 100 Shielders.
Kill 100 Tanks.
Reach level 5.
Reach level 10.
Reach level 25.
Reach level 50.
Lose 1 game.