All of the challenge related trophies are A LOT easier than they appear to be. The best strategy to approaching all of them is to first complete the campaign portion of the game with all upgrades for at least the Force Gun and Rivet Gun found.
Collectables Guide: http://www.playstationtrophies.org/forum/dead-space-extracti...
Then start the challenges on normal (higher difficulty levels do not impact your points), let most enemies get as close a possible to you without attacking and spam the Force Gun primary fire. This will ensure that you get the maximum amount of points per kill as it causes most of the necromorphs body parts to fly off in a single hit. The enhanced necromorphs (dark complexion versions of the slashers and leapers) take 2 close hits from the Force Gun to kill. You may want to keep a slight bit more distance between you and the pregnant necromorphs during the first shot due to the swarmers that charge out. Immediately shoot it a second time to kill all the swarmers and then shoot it a last time to kill the pregnant necromorph off ( you can just shoot its legs out to avoid the swarmers but I believe you get 250 points per swarmer killed by doing it this way)
For Lurkers (the little 4 legged necromorphs that shoot from their 3 tentacles), a fully charged secondary shot from the Rivet Gun will be enough to one hit kill it. Lastly, the spitters can most easily be taken down by throwing their projectiles back at them using Kinesis (technically this can be done to the Lurkers too but personally, I didn't find it as effective).
Just make sure that you always keep an eye out for ammo and boxes some times hidden in the background of the maps. In the case you run out of Force Gun ammo, use charged alternate fire from the Rivet gun until you find more (normal difficulty tends to be the most generous when it comes to this).
credit to lukey52 for the collectables guide