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