After several of hours trying to figure out the requirement for the "old school" medal (there seems to be no description anywhere on the internet), I believe I have managed to narrow it down. Since I don't know the exact requirements, some of the steps may be unnecessary, but I know them to work for the purpose of getting the medals.
Here is what I did:
-went to setting and changed health to 50%(not required, but makes it go faster)
-played tournament mode
-teams off
-match number doesn't matter
-Bounty on (I am sure it doesn't matter, but I always had it on)
-Select first ship and first weapon.
-Used a second controller to make 1 extra player
-Use same ship and weapon for 2nd player (will help with mirror achievement)
- No bots
- Select default level (you can just keep tapping the button)
-Once the game starts, only use the regular gun (RT)
-Only fire at enemy from the sides/top/bottom of screen and have your bullet wraparound to kill the enemy.
-Bullet must kill the enemy (won't get the medal if the enemy dies while running into an asteroid).
Below is a video I uploaded showing it in action as well as video evidence of me getting the "old school" medals for my efforts.