You can monitor your level shift using the combat attributes tab, and tracking it during the fight. In doing so, I've noticed that the level shifts you get from them only last a brief time, regardless if you die or not.
There is also a bar called "Favor of the Well" (I believe?) that seems to go up and down through the fight. If you minimize the window it says "Favor of the Well(Regen)", leading me to believe the bar is tied to his regen rate. It also says in the little tooltip something to the effect of "The well will favor who is winning". Which may lend some credence to the theory that people dying increases his regen rate. (People dying -> increase in the bar -> regen goes up.)
As for beating him, both leagues I've run with managed to kill Tyrant. We got stonewalled at 36% for a good 4 minutes or so, but then got more co-coordinated on the light wells for a consistent level shift of +9, and had someone pop vengeance, and that managed to let us overcome his regen.
