Here I show the best way to get the A New Champion in the Brutal Club mode of Brutal Rage.
Easiest way I found is that you want to grab every enemy with Y and repeatedly press X to punch. Try and have a weapon on you so you can land an unblockable attack if they get to close or it doesn't grab somebody. Found this the safest solution as the enemies do a lot of damage and can block and interrupt your strikes. Jump kicking also takes to long to kill and the time runs out.
For the last boss on hard he takes 5 strikes with a weapon to kill with rage mode on. I expand on the solution and show what you can do if your rage runs our prior to killing him.