The only mission in the game is missable is, "The Big Prank" which appears after the mission where a few kids want you to do pranks on other people. Once you finish with that mission, you head towards your Dorm and start the mission. I'm not getting into any spoils, but at the end, you'll get a Red Ninja outfit.
Be sure not to pass out or fall asleep during the time being of, "The Big Prank". Also, be sure to make a few extra game saves, so in case you do, you'll have something to stand by on.