After you complete the game once, start a new game. Go to equipment and make sure you equip the glasses. You'll know if you did it correctly b/c the screen turns dark. For the bonus mission you must have all cards in the trophy room. Afterwards, click on the cards and you will get a simple mission. After you complete it, click on 'continue' in the trophy room and you should get the badge.
For some reason, the "Spare Parts" Power up kept releasing a small nut/gear that was terrorizing my UAVs. It kept pushing them up and I think damaging them but I think it was trying to heal them. Not sure if this is just on my game though. Also, it would actually be nice if all vehicles could scale well into the late game. Or maybe something like combining two or three vehicles to form one higher tier vehicle with parts of each that I liked. Maybe for a sequel? Do make one please.