The game isn't released till next month, but the demo is out on the XBL Market and it is amazing. Like ShadowX said, you could go the traditional FPS way and just get a headshot for a measly 25 points, OR, you could rack up 500+ points on an awesome Skill Shot. Skill Shots are ways of killing enemies which give you points. The better the Skill Shot the more points. You don't just do one Skill Shot you could do multiple ones.
Get drunk and kill enemies while you are Intoxicated.
Pop off a Green Freaks head and be filled with Toxic Love.
You can even shoot an enemy in the crotch, he will get down screaming and just finish him off with a kick to head, no Mercy.
In the demo, you only get to use 3 guns, the PMC (Peace Maker Carbine) which is an assault rifle. The Screamer which is a Pistol, feels alot like the Boltok Pistol in Gears of War 2. The Flail Gun which is two grenades attached to eachother by a chain, it can stick to surfaces and wrap around enemies. It will detonate after a short period of time or you can detonate it yourself.
Another weapon you get is the Energy Leash which is like a whip, you use it to pull enemies towards you, throw multiple enemies into the air or pull down ceilings on enemies.
You are also able to kick enemies which sends them flying in slow motion, you are then able to elaborate on your attack, you could use your PMC and get the Bullet Kick skill shot, kick him some more off an edge, kick him into some spikes or electrical wires.
There will be alot more weapons in the full game, more game modes and most likely alot of missions in Campaign.
I suggest you get on your Xbox, download the demo and try it out for yourself. Don't worry if you can't rack up more then say 4000 points, you will be so hooked on this game that you will try and increase your overall score and move up through the leaderboards. The more you play and practice the more skill shots you will find out and the more ways you can kill your enemies. It's funny and awesome.