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.
Disrupt Shay's daily routine
Take down Mog Chothra
Endure a tight situation as long as you can
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
Make a Spoon Sweat
Examine all breakfast options
Complete all rescue missions with zero errors
Inhibit a powerful entitiy
Hear 20 reasons why Gary won't grab that
Take Control of the Boom Arms
Travel to a forbidden location
Feed two different people a healthy snack
Complete Act 1 of Broken Age
Find 30 unique reactions to the Spoon
Return a missing spaceship part
Clear up a tangled situation in one attempt
Return a heavy duty spaceship part
Visit someone in jail
Commission a custom garment
Get a family member's help on a big project
Tell a great joke in one attempt
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.