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
Travel to a forbidden location
Inhibit a powerful entitiy
Take Control of the Boom Arms
Disrupt Shay's daily routine
Escape the Maidens Feast
Learn all you can about Sugar Bunting
Examine all breakfast options
Unlock all Broken Age Achievements
Make a Spoon Sweat
Complete all rescue missions with zero errors
Hear 20 reasons why Gary won't grab that
Get to know someone in a precarious position
Feed two different people a healthy snack
Endure a tight situation as long as you can
Take down Mog Chothra
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.