This Trophy is fairly simple and you should get it through the course of normal play. Some suggestions and watch-outs...
Selecting a Striker is good choice, many of them like Legolas have high damage Ultimates that will make getting this Trophy easier. You'll want to avoid Galadriel, Felgrom and Wulfrun as their Ultimates don't do any damage.
As a note, I got this Trophy with Sauron, his Ultimate damages all enemy Guardians. Just keep an eye out for a very low heath Guardian and pop your Ultimate. Easy Trophy!