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

Hiker (50 points): Complete Chapter 1 in Single Player.
Weatherman (75 points): Complete Chapter 2 in Single Player.
Tourist (75 points): Complete Chapter 3 in Single Player.
Spelunker (75 points): Complete Chapter 4 in Single Player.
Legionnaire (75 points): Complete Chapter 5 in Single Player.
Exterminator (100 points): Complete Chapter 6 in Single Player.
I sense... Co-op (50 points): Complete any Multiplayer Chapter as Abe on Xbox LIVE.
Some like it hot (50 points): Complete any Multiplayer Chapter as Liz on Xbox LIVE.
It takes two (100 points): Complete all Chapters in Multiplayer on Xbox LIVE.
Heads you win... (10 points): Defeat 25 enemies with Bambini Heads.
Boom-Boom (10 points): Defeat 25 enemies with Oni Clubs.
Angry Plumber (10 points): Defeat 25 enemies with Drain Pipes.
Egg-splosive (10 points): Defeat 25 enemies with Frog Eggs.
Armed and Dangerous (10 points): Defeat 25 enemies with Krieger Guns .
Chiropractor (10 points): Defeat 25 enemies with the Ape Spine.
Debt Collector (20 points): Find all the Artefacts.
Eye on the Prize (10 points): Find the hidden Artefact in Chapter 1.
Finders Keepers (10 points): Find the hidden Artefact in Chapter 2.
Watching the Missing (10 points): Find the hidden Artefact in Chapter 3.
I See You (10 points): Find the hidden Artefact in Chapter 4.
Artefact Appreciation (10 points): Find the hidden Artefact in Chapter 5.
Dear Diary (10 points): Find the hidden Artefact in Chapter 6.
Vertigo (10 points): Fall off cliffs 20 times.
Going Down (10 points): Defeat 50 enemies by throwing them off cliffs.
Prickly Personality (10 points): Defeat 50 enemies by throwing them onto spikes.
I Feel Lucky (10 points): Defeat 50 enemies with the Samaritan.
Goal! (10 points): Kick 50 Bambini Heads.

Additionally, there are four secret achievements, all of which are currently unknown:

Secret Achievement (50 points): Unknown.
Secret Achievement (50 points): Unknown.
Secret Achievement (50 points): Unknown.
Secret Achievement (10 points): Unknown.