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1. Finish Classic Mode as Link

2. Play 400 Vs. Matches

 

The easiest way to unlock him is probably to just play through classic mode with Link on easy mode. You will have to learn to use Link well enough to get through this and beat his animated alter-ego at the end. If you just can't stand mastering Link, there is always the Vs. mode option. Just keep in mind that it will take you a VERY long time to finish 400 battles. I will post more when I learn the best method to bring down Toon Link. Because you are using a very similar character to fight him, your best bet may be to avoid fighting him directly and just beat him down with items until you have a strong upper hand.

I have no idea why, but I played classic Mode for the first time with Pit, hoping to find Jigglypuff at the end of the game. When I saw the Challenger Approaching warning, the shadow looked a bit oddly shaped. To my surprise, it was Toon Link instead who attacked me. I had a stroke or three of bad luck and ended up getting blasted by an item and losing the challenge. I went through with Peach this time and Unlocked Toon Link. I had never cleared classic mode with Link so I have no idea what's up with that.