There are trophies asking you to derezz with the bomb, corruption, heavy, or the stasis disc. Choosing the type is not enough; you need to finish them off with a power move to get credit. Derezzing without finishing with a power attack will yield you a plain light disc kill.
To unlock the Unstoppable Program trophy, you must get the maximum hit multiplier (30). Go into a Data Station and fire up a Game Grid Match. Disintegration is the default option with Bots. Let the CPUs gather together since they don't seem to care about you at all, then use the basic X,X,X combo in a large gathering. Some single throws will count as 2 or 3. Continue until you hit 30.