His attacks involve turning into a ball, and either bouncing or rolling after Vexx.
To defeat him, Vexx must wait until the Mummy becomes dizzy from rolling around too much, and quickly rush over and hit him by either uppercutting him of simply using a ground attack. Aberaxis will speed up his own attacks if Vexx manages to hit him. Aberaxis needs to be hit three times.
Finally, if Vexx manages to defeat him, he will earn a Wraithheart.