Keep Boogan on one side of the arena - the enemy will only attack from the front. It's easier to fight back this way.

After defeating the wave, duck and roll - opponents will not spawn until you get up. Use this to heal (food in garbage cans) and recharge powers.

Jump backwards to dodge attacks and punch enemies at the same time! See video below. Using this, you can not receive damage and even not use powers until a wave with bombers and gunners. Just with your punches and jumps!

While using tornado, Boogan is invulnerable. Use this to get to the bombers and gunners and take them out!

Failed? Exit to the main menu before end of cutscene and try again! You will definitely succeed!

Also, some points in the skill tree provide benefits. The "Urgency" skill reduces damage taken. Perhaps something else is working ...

My video demonstrating "jump and punch" tactic (has input overlay).
Video by Frame

One, two, three.