*Note* This solution was carried over from the one I posted on TA for the XBox 360 version. It has been modified slightly for the PS3 version.
I discovered a way to save a lot of time when going for this trophy. Load up Chapter XIII - Checkpoint 2 (credit to MaurickShepherd on TA for the checkpoint location), and be sure you are playing on Easy. There will be 3 guards, one who walks towards you in the same room (don't worry, you start behind cover and he doesn't know you're there), and 2 in the room to the back left. Wait until the first guard gets right up next to your cover then come out and melee him immediately (be sure to use Triangle, and not R2 as it won't count toward this trophy - credit to ICECLIMBERS on TA). Here's the trick...don't kill him immediately. Instead, let the slow-mo scene play out, and just stand there pointing your gun at him. When the melee cutscene stops immediately press Triangle again, and let the melee cutscene play out again. By this time the other guards will be alerted and starting to come out of the other room, but I have found that I could usually get 3 melees out of the first guard before killing him without being shot by the others. Now repeat with guard 2, but be aware of guard 3's location. Lastly, take care of guard 3 the same way. Afterward pause and reload checkpoint. Melee animations seem to be random, but if you get the one where the guard ends up on the ground looking up at you, be sure to tap Triangle repeatedly when the cutscene ends and you'll be able kick him 3-4 times before he dies...ALL OF THESE KICKS COUNT AS MELEES, so be sure to get as many kicks in as possible on the downed guard.
Every time you melee (or kick) a guard, it counts so you should be able to rack up at least 6-9 melees consistently before reloading. As a general rule, I tried to melee each guard at least twice, depending on health and enemy locations.
Things to keep in mind:
~Its been reported that this trophy is a bit buggy and may not unlock right at 100 kills, so just keep at it until it unlocks. If you haven't finished the single player melee grind, all of this will count toward that.
~There is a stash of 2 painkillers in the room with guards 2 and 3 but you may not bother with them as there's only 3 guards and you can reload the checkpoint at any time. This is also why accidental deaths aren't a huge deal, just reload and try again.
~You are vulnerable after the melee animation ends, so be sure to start tapping Triangle near the end of the cutscene so you can melee again and reduce your chances of being shot.
~I found that it is possible to shoot a guard in the leg/shin and have him drop, which will give you an opportunity to kick him repeatedly to rack up melees, but I couldn't do this consistently. You could try this option to mix things up a bit, but remember that guards die faster on Easy.