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