GigaBash

This can be done with 1 controller.

Go to Couch Play, then Battle.

Choose the first character as Thundatross, then hit right and add a CPU with Difficulty 6. Select Gigaman but be sure to select the same color as P1 using the button (L3). Then hit right and add 2 more CPU Difficulty 1 characters, again with matching colors (different from P1 and first CPU). You should have 2 characters on 1 team and 2 on the other (I had Red and Yellow teams).

Press to go to stage select.

Hit down to go to Match Settings. Set HP to 1%, Life Stack to 1. This will allow you to kill both opposing CPUs with a single hit.
Choose whatever stage you want. I chose Kimura District and we all started close to each other.
When the match starts, just get close to the nearest enemy and hit . With the difficulty set to 1, I didn't lose a single life the entire time. You should kill each enemy in 1 hit, and your Gigaman CPU should also help out. Just mash to rematch when both opposing CPUs are dead, complete 10 matches, and the achievement will unlock.