I was wondering if there was a way to reset the NG+ boss "Neo Khidr." For some reason it will not let me use a new heir in fighting the boss. Every time I enter the blue ghost-like door, it reverts back to an older heir that previously died, but is too weak to defeat the boss. Is there any other way I can fight the NG+ boss with a new character?

Neo-Khidr isn't actually an NG+ boss but a special version of the boss unlocked by receiving a special obol. When you start a new game after turning in the special obols you will be able to fight the regular version of the boss only once - as it has always been - but once you defeat the regular version their door will turn into a ghost door where you can fight the special boss as many times as you'd like. These were added in 1.2.

http://rogue-legacy.wikia.com/wiki/Special_Items - See the section at the bottom describing the special boss obols.

So basically there's no way to get a new character to fight Neo-Khidr? It's always going to be the same extremely low-level character? With the low-level character I'm stuck with, the HP was like 70 and it's pretty much impossible to beat the boss as a result.

Yeah it was designed to be extremely hard. You get as many attempts as you want and once you've unlocked the obol bosses they stay unlocked forever on that file. You only need to defeat the normal version first to get the ghost door.

I think their goal was to force you to use the skills of the character instead of grinding levels or gear. The biggest problem I have is the low hp. I think you only have enough life for about 3-4 hits in each obol boss. My character is level 407 (NG+3) and I have yet to beat one of these bosses.