Basically you draft the same as a normal arena. When you start the difficulty is set to normal. After 8 wins, the run is not over, instead you start another 8 battle series on the next difficulty up. This would continue all the way through Warlord 4.
After each 8 battle run, when you complete that difficulty, you get to add 2 traits to your team. You would be able to choose any 2 traits to activate. This would make it easier to account for the stat increases as the difficulty increases.
Another option would be at the end of each difficulty, you can choose 1 of 3 legendaries to replace a current member of the team. That way you could build up to a team of 4 legendaries.
I think this could add some more excitement to the arena and also allow for greater rewards for those able to get deeper through the gauntlet.