The strategy for this level/boss is the same for all categories. The level starts with a cutscene which cannot be skipped. Once the cutscene has ended, head through the door on the arena floor and up the stairs in the following room to the upper floor.
The boss fight has four parts, but can be divided into two sections. The first section is when the boss is a triceratops. All you need to do is run/speed glitch around the edge of the arena and you can easily avoid the attacks. Eventually the brain will exposed. Climb up the triceratops back and damage it. You do this two times.
After the first section the dinosaur bones will rearrange into a pterodactyl. Equip the pistol and then just do the same thing. Run around the arena until it floats in the centre and exposes its brain. This time you, need to fire continually - you should be easily able to reduce it from 400 to 200 and then 200 to death, even before any of the spawning dinosaurs reach you.
There is a health fountain on the upper level you can use whilst the boss is attacking you and not vulnerable - that way it wastes no time.
It is possible to clip through the rubble in the boss arena and finish the level without fighting the boss. This, however, is extremely difficult, due to the angle in which the camera faces and is almost impossible in a normal human run.