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