This may seem like a pain to get, but believe it or not, it's fairly simple. First things to note is what considers damage:

Damage to ANY worm, including your own will go towards this trophy

With that in mind, to get this trophy you essentially need to find the best level with most worms next to a single area and then you need to keep killing them. The best place that I found was at the beginning of Challenge 19. As soon as you start, what you need to do is switch to the Jet Pack and fly to the right. Here you'll find a bunch of worms. Drop a dynamite right in between the second/third Worms that you see there (closer to the Third). Now you can fly off to the right and kill yourself (yes kill yourself).

Wait for the dynamite to explode, and it'll send a couple of Worms flying and do damage enough to kill a couple more. This should have dealt around 400-500 damage if not more. So what to do now? Press Start, and select yes to restart.

Keep doing this again and again and you'll get the trophy (yes you don't need to actually win the game to get the trophy, just deal the damage and it's recorded).

An alternate way is to again go onto the beginning of Challenge 19, and instead use a Kamikaze run right through ALL of the enemies sitting on that ledge, this should get a whole lot more of them than via a dynamite.

It should also be mentioned that this tactic can also result in a lot of worms being wasted.