Do I lose two levels just for choosing to fight King Tut?
No, the loss of 2 levels is part of the bad stuff that happens when you normally fail to escape, or since the card specifically states it, &quot;even if they escape.&quot; From the World if Munchkin FAQ,

Q. King Tut and the Wight Brothers say &quot;Characters of higher Levels [than 3] lose 2 levels, even if they escape.&quot; Does that mean you lose two levels even if you defeat those monsters?
A. No. But if you cannot defeat them, then you must try to run away, and you'll lose the 2 levels even if you do escape. If they catch you, of course, you do suffer the Bad Stuff from those Monsters. (But you don't lose the two levels twice!)