Here is the full list of all 22 Time Carnage trophies - there are 7 bronze, 6 silver, 8 gold and 1 platinum.
Kill 1000 Dinosaurs.
Played all modes
Complete 4th Millennium on story
Kill 1000 Zombies.
Get 500 Headshots.
Acquire all trophies.
Achieve Bronze in all challenges.
Complete the story on "Easy" difficulty.
Complete Mesozoic Era on story
Complete 4th Century BC on story
Complete 6th Millennium on story
Achieve Silver in all challenges.
Complete the story on "Normal" difficulty.
Take no damage for an entire level in the story mode.
Shoot 250,000 bullets.
Survive 25 waves in Arcade
Kill 1000 Skelton Army.
Kill 1000 Robots.
Achieve Gold in all challenges.
Complete the story on "Hard" difficulty.
Unlock all the weapons.
Unlock all the perks.