There are two major things here to be able to defeat the City 2 Boss in just on cycle.

1. You have to land 2 double hits on their first fist attack
2. The difficult part, land a hit from the ground

This is only possible with a perfect double jump attacking on the highest spot and syncing it with the boss movement so it's on its lowest point. It seems hard, I was never able to replicate, but it is possible.