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

Hunter (10 points): Kill 500 enemies.
Predator (50 points): Kill 1000 enemies.
Headache (20 points): Kill 200 enemies with headshots.
Major League (20 points): Land 200 combo throws.
Cut a Rug (20 points): Land 100 full combo attacks (3 consecutive hits).
Ninja Style (20 points): Filena killed 50 enemies.
Privacy Issues (10 points): Destroy 1 Watcher (1/50).
Stop Looking At Me! (30 points): Destroy 20 Watchers. (20/50).
Leave Me Alone! (50 points): Destroy 50 Watchers (50/50).
Novice (5 points): Obtain the rank of Novice.
Soldier (10 points): Obtain the rank of Soldier.
Mercenary (20 points): Obtain the rank of Mercenary.
Commando (20 points): Obtain the rank of Commando.
Elite (20 points): Obtain the rank of Elite.
Slayer (20 points): Obtain the rank of Slayer.
Berserker (30 points): Obtain the rank of Berserker.
Storm (30 points): Obtain the rank of Storm.
Immortal (50 points): Obtain the rank of Immortal.
Lone Gunman (20 points): Kill all members of the opposing team alone (8-player Team Battle).
All Mine (20 points): Kill all other players in an 8-player Deathmatch.
On a Roll (20 points): Kill 10 opponents in a row during one match.
Killing Spree (20 points): Kill 20 opponents in one match.
Triage (20 points): Revive 10 teammates in one match.

Additionally, there are 27 secret achievements:

Pierce the Skin (5 points): Clear The Root of the Tower.
Through the Viscera (5 points): Clear Trachea.
Xylem (5 points): Clear Lumenosynthetic Reactor 2.
Fetus (5 points): Clear The Womb.
Clear Your Mind (5 points): Clear Cavitas Cranii.
Dermal Lesion (15 points): Clear The Root of the Tower on Hard.
Internal Trauma (15 points): Clear Trachea on Hard.
Phloem (15 points): Clear Lumenosynthetic Reactor 2 on Hard.
Breech (15 points): Clear The Womb on Hard.
Subdural Hematoma (15 points): Clear Cavitas Cranii on Hard.
Enlightenment (15 points): Clear The Seed of Gnosis.
Death & Rebirth (30 points): Clear the entire game on Hard.
Professional Exterminator (20 points): Kill the Gargantua on Hard in 2 minutes 30 seconds or less.
Steady, Steady... (20 points): Shoot an enemy with a Plasma Lancer from 50m.
Five Birds, One Stone (20 points): Hit 5 enemies with one shot from the Ifrit.
Killing Connoisseur (30 points): Kill 10 enemies with every firearm Syd can equip. (Melee kills don't count.)
Matador (20 points): Kill the Dreadnought on Hard in 2 minutes or less.
Fight Fire with Fire (20 points): Shoot down 10 projectiles from the Raven.
Getting Intimate (20 points): Kill 100 enemies with melee attacks using the Bloodcleaver.
Gladiator (20 points): Kill the Chariot during Thorax on Hard in 1 minute 30 seconds or less.
Warrior (20 points): Defeat Thanatos on Hard in 1 minute 30 seconds or less.
Nevermore (20 points): Kill the Raven on Hard in 2 minutes or less.
Entropy (20 points): Defeat Chaos (Thanatos II) on Hard in 1 minute 30 seconds or less.
Trusty Sidearm (30 points): Clear the entire story using only the Revenant.
Release (20 points): Defeat Diablosis Soma (Thanatos III) on Hard in 3 minutes 30 seconds or less.
What a Pal (20 points): Don't let any teammates who were setting charges go down during the final battle in The Womb.
8 Seconds with Style (20 points): Kill all enemies in Trachea without dying.