Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Paid in Fyrestone (5 points): Complete 5 missions in the Arid Badlands.
Made in Fyrestone (15 points): Complete all missions in the Arid Badlands.
Paid in New Haven (10 points): Complete 5 missions in the Rust Commons.
Made in New Haven (20 points): Complete all missions in the Rust Commons.
My Brother is an Italian Plumber (15 points): Kill an enemy by stomping on its head.
Speedy McSpeederton (10 points): Race around the Ludicrous Speedway in under 31 seconds.
You call this archaeology? (20 points): Apply an elemental artifact.
Ding! Newbie (5 points): Earn level 5.
Ding! Novice (10 points): Earn level 10.
Ding! Expert (20 points): Earn level 20.
Ding! Hardcore (30 points): Earn level 30.
Ding! Sleepless (40 points): Earn level 40.
Discovered Skag Gully (5 points): Discover Skag Gully.
Discovered Sledge's Safe House (5 points): Discover Sledge's Safe House.
Discovered Headstone Mine (5 points): Discover Headstone Mine.
Discovered Trash Coast (5 points): Discover Trash Coast.
Discovered The Scrapyard (10 points): Discover The Scrapyard.
Discovered Krom's Canyon (10 points): Discover Krom's Canyon.
Discovered Crimson Lance Enclave (15 points): Discover Crimson Lance Enclave.
Discovered Eridian Promontory (15 points): Discover Eridian Promontory.
Ding! Champion (50 points): Earn level 50.
Get A Little Blood on the Tires (20 points): Kill 25 enemies by ramming them with any vehicle.
Rootinest, Tootinest, Shootinest (10 points): Kill 5 Rakk in under 10 seconds.
Pandora-dog Millionaire (50 points): Earn $1,000,000.
Fence (25 points): Sell 50 guns to a shop.
Can't We Get BEYOND Thunderdome? (25 points): Win an arena match.
Duel-icious (15 points): Win a duel against another player.
Group LF Healer (25 points): Rescue a groupmate from death in a co-op game.
There's No "I" In "Team" (30 points): Complete 15 missions in co-op.
And They'll Tell Two Friends (10 points): Play in a co-op game with either an employee of Gearbox or someone who has this achievement.
Weapon Aficionado (20 points): Reach proficiency level 10 with any weapon type.
Duelinator (35 points): Win a duel without taking damage.
Facemelter (25 points): Kill 25 enemies with corrosive weapons.
1.21 Gigawatts (25 points): Kill 25 enemies with shock weapons.
Pyro (25 points): Kill 25 enemies with incendiary weapons.
Master Exploder (15 points): Kill 25 enemies with explosive weapons.
There are some who call me...Tim (25 points): Equip a class mod for your character.
Fully Loaded (10 points): Rescue enough Claptraps to earn 42 inventory slots.
Truly Outrageous (15 points): Kill an enemy with the Siren's action skill.
Careful, He Bites (15 points): Kill 15 enemies with the Hunter's action skill.
Reckless Abandon (15 points): Kill 15 enemies with the Berserker's action skill.
Down in Front! (15 points): Kill 15 enemies with the Soldier's action skill.

Additionally, there are eight secret achievements:

Secret achievement (30 points): Unknown.
Secret achievement (10 points): Unknown.
Secret achievement (20 points): Unknown.
Secret achievement (30 points): Unknown.
Secret achievement (40 points): Unknown.
Secret achievement (50 points): Unknown.
Secret achievement (35 points): Unknown.
Secret achievement (15 points): Unknown.