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