Here is the full list of all 16 Soul of Giga achievements.
Have your very first Giga
Invoke your first Giga
Get 3 Giga shards
Get 10 Giga shards
Get 30 Giga shards
Deal the total of 3000 damage to enemies
Open 10 chest
Open 1 Blue Chest
Acquire 5 hats
Acquire 5 vessels
Invoke Ogre Giga
Have Giga reached level 50
Have all the Gigas
Have all the Vessels
Have all the Helms
Defeat Captain Halberd