Output 12-25V from Arduino Mega
Use an H-bridge motor driver. They can use arduino signals to control higher voltages without damaging the arduino. Check out the  L298N from gearbest. It's cheap but will probably do the trick if you're not using too much current. 

It can supply about 1A through each gate at 5-30V. 

this video should help explain it. (I haven't watched the video but it seems like it got good feedback).