To stay at Level 3, you invoke the Yoshi Egg game and fail it intentionally. There's a couple items in the game that can summon the mini game, even during boss fights.
This is indeed a tough challenge given that you not only have to win the boss battles, but also win the egg roulette. I swear, I f***ed up about 10 times on Bundt.
This was also the challenge that made me realize that Smithy WAS more of a boss than Culex. Sure, Culex had his crystals and such, but I still could beat him in the Level 3 challenge without TOO much effort. Smithy on the other hand is WAY too goddamn tough in his final form.