From that time period, it was probably one of the Spider-Man games that tied in with the Raimi movies. It would have had Bruce Campbell narrating the tutorial levels, if that helps jog your memory.
The first one had a tutorial level in a wrestling match, but the second one sounds more similar to what you described. Unfortunately, if you were playing Spider-Man 2 on a Windows PC, it means you were playing the worst possible version of a great game. The Playstation version was far superior in performance, controls, graphics, and well just about every other way. The Windows version (you can’t even call it a port, because it was an entirely different game) was developed by Fizz Factor. If you tried to play the game today, I would strongly recommend the Treyarch version on an emulator, but it might not have the nostalgia factor.
Inb4 bigots call Birdo depiction “woke.”