Here is the full list of all 20 Lila's Sky Ark achievements.
Reach the Ending
Find the developer room
Break all Piñatas
Collect all petals
Find all Letters
Visit all rooms
Liberate the Spirit of the Deep
Defeat the Conductor
Find all Recipes
Liberate the Spirit of the Mountain
Liberate the Spirit of the Sky
Deliver all Attention
Open all Gifts
Free Mr. P
Defeat the Pianist
Liberate the Spirit of the Trees
First place on the podium
Defeat the Quartette
Defeat the Drummer
Boot up the Doctor