In this video guide I will show you how to win against Ripper the Roo in adventure mode and win a boss challenge without getting hit by any of the boss' power-ups.
Now to beat Roo, all you really need to do on easy is just pass him and make sure to stay ahead of him to avoid his attacks since they are only beakers. He will not throw them forward so once you pass him the only weapons on the ground you risk of running over coming back around is your own. There won't be much of a challenge on easy just do your laps and win.
Once you have done what I said above the achievement for not hitting his attacks will unlock after the race is over. Just be sure to pass him right away to be safe from running over his power-ups and you will be good. Just finish the race to get both achievements.