This are all the achievements you get while playing the game in this order.

Sneaky Thief
Steal the Lupine Twine Amulet from the Museum of Myths and Mysteries.


Junkyard Dog
Defeat Grim in his lair, deep in the Junkyard.


Honourary Mayor
Inspect the Mayor's office.


Sleuth
Give Judy enough evidence to get her a great scoop on Alphonse.


Explorer
Fill in all quick travel locations on your map.


Showdown
Sniff out Alphonse and defeat him once and for all!

An Essential Upgrade
Use the Pro Thief Kit to unlock a Secure Door.


After you defeated Alphonse there will be the credits. Although you can keep on playing. After some quests you will be rewarded with a Pro Thief Kit. With that you need to open one of the doors that has a security code on it. When first is opened your achievement will popup,


Get With the Times
Purchase the computer from Harvey and boot it up.


This can be bought at the harvey shop. You might need first to buy a desk to put the computer on.
After that you go to your house and go up the stairs, boot up your brand new computer and the achievement would popup.


Postal Hassler
Really scrutinise the apartment's post box.


This one is pretty simple. Just keep checking your post box outside your apartment, until the achievement pops up.


Fixated
Really get to know Detective Strump.


This one is pretty simple again. Keep calling Strump by pressing Z. Keep doing this until the achievements pops up.


Super Sleuth
Find every possible piece of evidence on Alphonse for Judy.


This will include the evidence from the main story. Although there is more to find, but for this you need the Pro Thief Kit. Their locations are:
1. One map left from Café District, inside the security door.
2. One map north of Lupin Twine Amulet Exhibition, inside the security door.
3. Thirth map east from the Museum Archives Guard, inside the security door.
4. One map north of Mansion Courtyard, inside the security door.
5. Two maps east and one north from Dragon Chamber, inside the security door.


Shop Till You Drop!
Clean Harvey out.


Simply buy everything inside Harvey's shop.


Retro-active
Watch the credits with the computer booted up.


Buy a PC and TV from Harvey. Boot the PC up and after that watch the TV (the credits).


The Whole Story
Watch the credits after helping everyone in Feyre.


Watch the credits after you have completed all quests (you can watch the credits again after you bought the TV from Harvey).


Obsessive Collector
Discover more of Feyre's picturesque history.


Find all pictures.