For the last challenge the difficulty ramp is quite ridiculous. I suggest moving your car at a steady, slowish pace near the left edge of the map (not directly at the edge as police cars might knock you unexpectedly). Then once the police cars come out just stall and wait for them to go in front. They will effectively help you to clear bombs and obstacles. As long as you are careful and keep up this method, you should be able to get the 6th gold medal.
Boss Rush guide: 1st boss stand on bottom of leftmost door and shoot to the right. 2nd boss: Stand in between the eyes and shoot left to right. 3rd boss: Gravity to adjacent side whenever he is about to move. Do this while shooting at him. Be patient and you will eventually beat him. 4th boss: Shoot him all the time, while jumping over the coloured doughnuts. Your projectiles will block his projectiles, so don't worry about those. 5th boss: Reflexes. When he is shooting those big waves make sure you get to the opposite side and shoot at him. When he is bouncing, stay at far left, just evade using gravity. When sleeping, stay at a corner, gravity to opposite lane at last minute. When he's shooting in a cyclical motion, just walk along the edges.
Whew 3:48 finally. Key to getting the badge is memorisation. The badge isn't hard enough to be an impossible, but is certainly harder than most hard badges. Anyway 5/5 considering it is such an old game, very creative.