I was playing Super Mario World on the Wii U the other day and my dad said that in order to "beat the game legitimately" you have to beat every level. How many levels are there?
Actually, you're dad was probably referring to finding all the exits from all the levels in the game
In the Super Nintendo version of the game, there are 96 exits total. These are tracked on the load game screen immediately after the title screen.
Finding all of them will put a star next to the exit count.