What was Jack in ME2? She more or less fits exactly what the OP is asking for, especially if you were a Renegade Shepard. I personally don't really care what the character's moral compass is as long as they have an interesting personality and are worth getting to know. Being nicer or meaner is irrelevant to me.
Jack's a pretty bad example. Horrible, really, on multiple levels.
First and foremost, she's a woobie. No, that doesn't really capture it- in a cast full of woobies, she is the woobie, the one whose backstory was specifically created and exagerated to explain and justify who she is and make her sympathetic despite anything else. Torture without cause, involuntary drug use, pavlovian conditioning, both explicit and implicit abuse of emotional, physical, and possible (IIRC) sexual nature. Jack isn't a dark badass who owns her abilities and nature- they were forced on her, and she never wanted them. Emotionally and ethically, she's a scared and desperate kid who doesn't want to be hurt by others yet again.
Moreover, her character arc centers on normalization and healing, not rationalizing or defending who she is. While ME2 leads of with a Renegade-esque path of accepting herself as a killer, ME3 overrides that to return it to the Paragon path of normalization and healing. This isn't a bad thing for Jack, the character, but it isn't a 'dark' or 'evil' characterization route either. It's character railroading in entirely the opposite direction. Even when she's supposed to be 'edgy' and 'badass' compared to her students, her characterization doesn't present anything more immoral than some f-bombs and a soft strike on the PC. Her morality is pretty conventional, and even in ME2 if she had her druthers she wouldn't have done most of the stuff she did.
Speaking of which... all her alleged villainy is utterly off screen. Heck, we don't even get to see Jack actually destroy those mechs in her own introduction scene, and the trail of destruction we see is implied to be hers but we never see that sort of power or chaos from her again. Despite her fearsome reputation, the sort to make hardened killers scared and afraid, she never actually does anything partiuclarly immoral or unethical. The best she gets is her cat fight with Miranda... but in the end it's just words. Just like all her stories and boasts are words, told rather than shown, and many of which were suspect. And what we do know that isn't just words...
Well, there was a really strong tendency by the writers to basically imply that anyone Jack fucked with, deserved it. Or that at least it wasn't her fault, or that she was a victim in it at all, and basically anything that could be used to make the blame not hers. None of Jack's crimes come with a body count or anyone who could be confirmed as innocent, and they fall into two broad categories: Jack being used and abused by real criminals, or Jack getting revenge on someone who fucked with her first. In many respects, Jack's presentation is all talk, or justified, to the point that I once incensed a number of Jack fans with the mere suggestion that she could be a murderer or have initiated significant crimes of her own volition. They challenged me to find even one point in the games that indicated she ever did anything for personal enrichment (past survival and fleeing) or just for the lols (which she implies, but is never validated), and... I couldn't. Jack never does, and is never claimed to have done, anything unnecessary against anyone who didn't deserve it (by being a scumbag or hurting her first). There's not even any substantiated charges of collateral damage and civilian casualties, which is whack.
Given what the OP is looking for... Jack definitely isn't it.