Here is the full list of all 15 Giga Girl achievements.
Find the Blue spare head
Find the Rainbowroid
Defeat King Crab
Find the Star wand
Destroy the Purple Room
Defeat Cone Giant
Defeat Ruby Assassin
Defeat Yellow Subman
Defeat Rocket Bandit
Defeat Fire Inferno
Defeat Vacuum Cyclops
Find the Green mushroom
Find the Triple triangle
Find the Bomb