There are 21 Trophies that can be collected.

BRONZE

Bulldozer
You bulldozed 10 buildings

Cosmic Bulldozer
You destroyed 30 buildings.

Galactic Bulldozer
You destroyed 100 buildings

Car Collector I
Wrecked 20 cars.

Car Collector II
Wrecked 100 cars.

Car Collector III
Wrecked 500 cars.

Air I
You jumped 400m.

Air II
You jumped 500m.

Barbecue
You grilled 10 cows.

Chef
You grilled 30 cows

Gourmet
You grilled 100 cows.

Amateur Driver
You drove a car for 10s.

Professional Driver
You drove a car for 20s.

Expert Driver
You drove a car for 60s.

Oily wheels
You drifted with a car 10s.

Slider
You drifted with a car 30s.

Drift King
You drifted with a car 60s.

City Eater
You levelized 1 city.

City Muncher
You levelized a city with all stars.

City Dominator
You levelized each city.

Earth Crusher
You levelized each city with all stars.

http://www.ps3trophies.org/game/demolition-inc/trophies/