How to amplify a 0-5V PWM Signal to 0-12V, 10A
Step up converters don't have a gain and most of them are built to operate within specific input\output ranges. Variable voltage step ups may be difficult to control. 

I think the best thing would be to find an off the shelf AB amplifier if you wanted to 'amplify' PWM

Another option would be to parallel op amps. Paralleling op amps, like the LT1210 (1.2A of current) or the OPA548T (~2A of current). The drawback would be some loss in power and you would need at least 5 opamps.

The best thing would be to drive an H-bridge or mosfet with the arudino as H-bridges are great for PWM and have low loss. The other nice thing about mosfets is they have almost any power limit through paralleling.