Here is the full list of all 11 Robotry! achievements.
Complete World 1, Lonely Legs Cellar
Complete World 2, Hyper Jungle
Complete World 3, Apple Juice County
Complete World 4, Animal Day Spa
Complete World 5, Puddle Knights Museum
Complete World 6, Gravity Gardens
Find all the secret heebos and reunite with the captain
Skip the first secret heebo by not falling into the pit
Found a secret area
Complete World 1, Lonely Legs Cellar in shared robo mode
Complete World 6, Gravity Gardens in shared robo mode