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