You have to complete the story before you can get this achievement.
Lilac is the little monkey and probably kid of Pink (the monkey you play in the Story) and Yellow - you play him/her after the story.
After completing the game, start a liberation run (the left button - not daily) and progress a bit.
A symbol with the hornbill-icon will appear. Touch the cage to free the hornbills. Missed one? No problem, there are an infinite number. Just keep swinging. You can leave and come back later - you can even die. Your progress is saved.