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