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