Although ExsphereBrawler's solution is completely valid, I have an easier way to get this done with just a level 1 character, meaning all those "Extended Combo Time" bonuses are not required.
Once you unlock Barragan, take him into Mission 3 (timed mission). Here you have a lot of enemies in a very enclosed area.
Now, I know Barragan is extremely slow, but he has one move that makes him a combo beast: Respira. Jump and press triangle to unleash this move that will do continuous damage to enemies for a few seconds. Bunching enemies up and using Respira will increase your combo as well. And the best thing about Respira for this trophy? It takes FOREVER for Respira to kill anything, even on normal!
All I did was use Respira, move around (to recharge my spirit gauge, just to be safe), and repeat. I had a 2,000+ hit counter before I got to the boss at the end of the mission.
Do not, under any circumstances, use your ignition trigger. I got into the habit with characters like Stark and Ichigo to use my ignition to increase attack power, and that works with Respira too. It will kill enemies too fast leaving you scrambling for something else to hit.
Below is a video that demonstrates how to build a fast combo with Barragan. Credit goes to BitingLion. If I missed anything please leave a comment.