Here is the full list of all 45 Broken Age achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Execute a PERFECT escape
Complete all rescue missions with zero errors
Start a group dance party
Make someone strut their stuff
Get to know a stranger
Answer some tough questions quickly
Tell a great joke in one attempt
Clear up a tangled situation in one attempt
Find 30 unique reactions to the Spoon
Endure a tight situation as long as you can
Feed two different people a healthy snack
Learn all you can about Sugar Bunting
Hear 20 reasons why Gary won't grab that
Make a Spoon Sweat
Travel to a forbidden location
Take Control of the Boom Arms
Inhibit a powerful entitiy
Disrupt Shay's daily routine
Examine all breakfast options
Take down Mog Chothra
Leave an isolated town
Reunite a mother and child
Get to know someone in a precarious position
Escape the Maidens Feast
Complete Broken Age
Talk to the boss
Stand up for someone even though you haven't met him
Stand up for someone even though you haven't met her
Complete Act 2 of Broken Age
Find a genius
Chart a course away from danger
Return a missing spaceship part
Follow up on a successful performance
Visit someone in jail
Get a family member's help on a big project
Deploy a weapon of mass destruction
Uncover an unsavory scheme
Reconnect with some old friends
Remove 8 sad faces from the Bassinostra
Get to the ship's brain
Commission a custom garment
Return a heavy duty spaceship part
Complete Act 1 of Broken Age
Unlock all Broken Age Achievements
Complete Broken Age in under an hour, not counting loading and paused gameplay.