Most levels are littered with secrets (the first level containing 8 by itself) and you'll need to get 70 secrets to unlock another trophy. The first chance to get this is in the first level, Hollywood Holocaust, From the start, hop down the chute and take out the enemy on the crate. Hop onto it and from there hop onto the ledge nearby and onto the back wall. A rocket launcher will raise up. Grab it to unlock this trophy.
3D Realms has an excellent walkthrough for the first four episodes that detail all of the secrets and how to get them at
http://legacy.3drealms.com/duke3d/walkthrough/.
You'll also get this on your quest for the following trophy: