Instructions
Method One: Playing Brawl Matches
Play 300 "brawl" matches. The easiest way to do this is to play short one-life matches against the computer.
From the main menu, start a brawl match.
Set the match type to stock and the stock amount to one.
Choose one computer opponent and disable the other two.
Select a stage you can fall off of.
Start the match and immediately jump off the stage. Repeat this 300 times, and Sonic will appear. This method is tedious and time-consuming.
Method Two: Playing Single Player Modes
Choose one of the following steps.
Play through the "Subspace Emissary" mode until Sonic joins your team. This will take some time, but it's a fairly engaging game mode with some variety.
Or beat "classic mode" with 10 different characters. This is probably the quickest, easiest and most fun way to unlock Sonic.