Similar to the trophy in Alien Breed 2, you must play a Survivor Mode map by yourself and survive for at least 8 minutes. Keep in mind that items and weapons will spawn all over the stage every half a minute or so.
I recommend playing on the Onslaught Map, using nothing but the assault rifle. Go around the stage in a clockwise motion and pick up everything you run across, even if you don't need it so new items can spawn in its place. Don't be afraid of running out of ammo, keep spraying bullets at aliens as it'll stun them and hold them into place. Use a stun grenade if you find yourself facing more than you can handle at once. I don't suggest you camp in one corner of the stage as you'll run out of ammo pretty quickly. Keep your health up at all times; you can use a health kit and fire a weapon at the same time.
Survive for 8 minutes or more and the trophy will unlock upon exiting the end results screen.