Tell her that her character is a Sue. Telling her to ignore the people telling her that she's got a bad character makes you part of the problem and will make people view you as a synchophant at best.
Honestly, if treading lightly hasn't helped, continuing to tread lightly won't help her improve. Sometimes you just need to break out the hammer and show the wrath of the editor god.
And if she thinks that telling her that her character is boring/unlikable/unrealistic is an attack on
her, you may want to introduce the concept that IC=/=OoC. Heck, send her to the
Bad RPers Suck LJ comm and tell her that she could stand to read over some of the entries. If you want more specific entries I'd be glad to help, but it'll take a bit to dig up the ones suited to your situation.