Achievements are unlocked by accomplishing the listed task and will give you the listed number of gamer points. If you have an X-Box 360 gamertag, you can log in using this same gamertag and the gamerpoints/achievements will count the same as if you were playing the 360 version / any other X-Box 360 game.

Agatha's Song (20GP):
Completed "Agatha's Song"

Ambassador of Peace (20GP):
Reached Level 14 with Good Karma

Big Trouble in Big Town (20GP):
Completed "Big Trouble in Big Town"

Blood Ties (20GP):
Completed "Blood Ties"

Data Miner (20GP):
Hacked 50 terminals

Doesn't Play Well with Others (20GP):
Killed 300 people

Escape! (20GP):
Completed "Escape!"

Finding the Garden of Eden (20GP):
Completed "Finding the Garden of Eden"

Following in His Footsteps (20GP):
Completed "Following in His Footsteps"

Galaxy News Radio (20GP):
Completed "Galaxy News Radio"

Harbinger of War (20GP):
Reached Level 14 with Bad Karma

Head of State (20GP):
Completed "Head of State"

Keys are for Cowards (20GP):
Picked 50 locks

Last, Best Hope of Humanity (30GP):
Reached Level 20 with Good Karma

Mercenary (10GP):
Reached Level 8 with Neutral Karma

Oasis (20GP):
Completed "Oasis"

One-Man Scouting Party (20GP):
Discovered 100 locations

Paradigm of Humanity (30GP):
Reached Level 20 with Neutral Karma

Picking up the Trail (20GP):
Completed "Picking up the Trail"

Pinnacle of Survival (20GP):
Reached Level 14 with Neutral Karma

Protector (10GP):
Reached Level 8 with Good Karma

Pychotic Prankster (10GP):
Placed a grenade or mine while pickpocketing

Reaver (10GP):
Reached Level 8 with Bad Karma

Reilly's Rangers (20GP):
Completed "Reilly's Rangers"

Rescue from Paradise (20GP):
Completed "Rescue from Paradise"

Scientific Pursuits (20GP):
Completed "Scientific Pursuits"

Scourge of Humanity (30GP):
Reached Level 20 with Bad Karma

Silver-Tongued Devil (20GP):
Won 50 Speech Challenges

Slayer of Beasts (20GP):
Killed 300 creatures

Stealing Independence (20GP):
Completed "Stealing Independence"

Strictly Business (20GP):
Completed "Strictly Business"

Take it Back! (40GB):
Completed "Take it Back!"

Tenpenny Tower (20GP):
Completed "Tenpenny Tower"

The American Dream (20GP):
Completed "The American Dream"

The Bigger They Are... (20GP):
Kill all the Super Mutant Behemoths

The G.O.A.T. Whisperer (10GP):
Took the G.O.A.T.

The Nuka-Cola Challenge (20GP):
Completed "The Nuka-Cola Challenge"

The Power of the Atom (20GP):
Completed "The Power of the Atom"

The Replicated Man (20GP):
Completed "The Replicated Man"

The Superhuman Gambit (20GP):
Completed "The Superhuman Gambit"

The Wasteland Survival Guide (20GP):
Completed "The Wasteland Survival Guide"

The Waters of Life (20GP):
Completed "The Waters of Life"

Those! (20GP):
Completed "Those!"

Tranquility Lane (20GP):
Completed "Tranquility Lane"

Trouble on the Homefront (20GP):
Completed "Trouble on the Homefront"

Vault 101 Citizenship Award (10GP):
Got the Pip-Boy 3000

Vault-Tec C.E.O. (30GP):
Collected 20 Vault-Tec Bobbleheads

Weaponsmith (30GP):
Made one of every custom weapon

Yes, I Play with Dolls (10GP):
Collected 10 Vault-Tec Bobbleheads

You Gotta Shoot 'Em in the Head (20GP):
Completed "You Gotta Shoot 'Em in the Head"