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