Here's a solution that's doable at the very beginning of a chapter and doesn't require any upgrades.
Start Chapter 3 on Easy. Tripp will almost immediately scan to reveal three 'unconscious' mechs, and the one closest to you will begin calling for reinforcements. It doesn't matter if you kill the other two, but if you can do it quickly without accidentally killing the one calling for reinforcements, it makes it a whole hell of a lot easier.
While the reinforcement counter is ticking down, damage the mech until he's got the red sparks, which means he's near death. Position yourself so that the roadblock (near the shipping container) is between you two so he can't run up and whallop you as easily. Pull left trigger to aim your staff, and keep it trained on him. Blast him when the timer gets to 1 second.
If you fail, restart the checkpoint and try again. You can use Back to skip the cut scenes. I had it on the first try that I used the roadblock to keep him away from me, and had only managed to kill 1 of the other mechs.