The medals work. You are allowed to use Pistol and health upgrades but are not allowed to buy other weapons for the pistol run.
I have to rate -1 star because the game didnt spawn the last enemy at level18. Then I quit to menu and got reset at lvl 19 but with no pistol upgrades. Miraculously survived (you can use the honey pot even with 0 honey left) and then lvl 20 was normal.