Nice sprites and animations. The coliseum style made me instantly remember of Swords and Sandals.
As others have already pointed out, in the second run the attack stops working, and it would probably be better if the gladiator and the bear doesn’t spawn in the same point.
I think a screen that shows who won would also improve the gameplay, and maybe(if it won’t interfere in menu when it works) start the game by pressing spacebar instead of using the mouse.
It is fun to play and has nice sprites that both looks great and fits the limitations. Great job both of you