This can be done on a 10-person Rumble and on the Easy difficulty setting if you so wish. I personally used Andre the Giant, but any of the super heavyweight characters should be sufficient.
The quickest method to eliminate opponents, without having to weaken them and to avoid the ring filling up too much, is to irish whip your opponent to the top right or top left turnbuckle, perch them on the top rope by pressing the right stick upwards, and then use a running strike to eliminate them immediately.