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.
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
Follow up on a successful performance
Tell a great joke in one attempt
Return a missing spaceship part
Return a heavy duty spaceship part
Clear up a tangled situation in one attempt
Deploy a weapon of mass destruction
Reconnect with some old friends
Get to know a stranger
Remove 8 sad faces from the Bassinostra
Uncover an unsavory scheme
Get to the ship's brain
Complete Act 1 of Broken Age
Unlock all Broken Age Achievements
Make a Spoon Sweat
Examine all breakfast options
Disrupt Shay's daily routine
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
Endure a tight situation as long as you can
Take down Mog Chothra
Find 30 unique reactions to the Spoon
Visit someone in jail
Commission a custom garment
Get a family member's help on a big project
Find a genius
Answer some tough questions quickly
Execute a PERFECT escape
Talk to the boss
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.