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.
Make a Spoon Sweat
Endure a tight situation as long as you can
Feed two different people a healthy snack
Complete Broken Age
Talk to the boss
Stand up for someone even though you haven't met him
Stand up for someone even though you haven't met her
Complete Act 2 of Broken Age
Find a genius
Visit someone in jail
Return a missing spaceship part
Chart a course away from danger
Return a heavy duty spaceship part
Get a family member's help on a big project
Commission a custom garment
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
Answer some tough questions quickly
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
Inhibit a powerful entitiy
Take Control of the Boom Arms
Travel to a forbidden location
Escape the Maidens Feast
Learn all you can about Sugar Bunting
Disrupt Shay's daily routine
Examine all breakfast options
Unlock all Broken Age Achievements
Complete all rescue missions with zero errors
Hear 20 reasons why Gary won't grab that
Find 30 unique reactions to the Spoon
Clear up a tangled situation in one attempt
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
Start a group dance party
Complete Broken Age in under an hour, not counting loading and paused gameplay.