This is extremely easy to get. Interestingly enough, if you do it the way I've described below, it doesn't cost any credits. You don't have to actually buy anything with in game credits.
From the main menu, go to World Tour. Go to Customize Bike. Go to on Appearance. Go to Mirrors. The default is 'stock side mirrors' and 'remove side mirrors' is immediately left of the default. Click on Remove Side Mirrors and the achievement will unlock. It does not cost anything. The game apparently believes 0 CR is an actual price.