I'd have to say that this is one of the most iconic (and practical) quests out there for Hunters.
The whole lore of the quest, is that you hunt down many foes, and then when you prove yourself, you go after the strongest mobs of that type, and anyone who can triumph over this challenge, is quite a skilled hunter.
With that being said, I managed to solo all of Nesingwary's Quests, including "The Ultimate Bloodsport".
Let me tell you, that was freaking hard as Nuts. I wish I had screenshots to prove it, and I understand if you don't believe me on this, but I'll tell my story (and strategy) anyways.
I'll start off by saying that I've never tried a tank pet. I used a Cunning pet for this, I'm thinking that a Tank pet may not put out the kind of DPS you need (you will likely run out of mana before the fight is done), and that a DPS pet will take too much damage, and will die before Tusker is dead.
So, I am going to include my strategy here.
Using the data that I've observed from my three fights (I failed the first two times), I'm fairly sure that a Draenei is the one and only race that can do it, at least without using fully decked out and enchanted dungeon blues. Gift of the Naaru is the star player of this battle, to be sure. Without it, I would have never even come close, my pet would have been dead at 30%. I used a Ravager for this fight, I do not know whether or not another Cunning pet would have done the trick. Also, Wolverine Bite is a must. Stun is a must in this fight.
So basically, here is how it went:
1). First, I had to clear the two Bull Elekks near her "mountain". An add would mean certain failure, to be sure. Tusker is only a Group 2 quest, but damn. I wonder just what went through Blizzard's mind when they did that; this little girl was harder than some Group 3 quests I managed to solo.
2). Second, I laid down an Immolation trap and made sure all of my cooldowns were up, from the previous fight. I knew I needed all of the DPS I could possibly muster on her, and 1,099 damage is nothing to laugh at. She has roughly 32,700 if I recall. That might seem small, but as you will see later, I would have died if it weren't for that trap.
3). Next, I put a Hunter's Mark on her. This may seem trivial and "you should do that anyways", but I'm one of those hunters who rarely use it outside of fighting Elites; it uses up too much mana, and any hunter knows how precious Mana is to our XP/hr.
4). Now it was time to take a deep breath, and go over everything in my head. Cooldowns up? Yes. Pet full HP? Yes. I'm full HP and Mana? Yes. Okaaaay. Let's do this. I start off with a Scorpid's Sting. The first two times, I tried using Serpent's Sting, but it just wasn't working out for me. Amazingly, I noticed the difference big-time with Scorpid Sting, and I'd have to say that this is the way to go. 3% doesn't sound like much, but I noticed it. A lot.
5). I knew that I couldn't wait for my pet to go down in health before using my first Mend Pet; Mend Pet cures for 383 per tick at Lv68. Tusker melees for over 500 per hit, some criticals reaching as high as 1,300. If you wait until your pet is missing a chunk of HP, it is already too late. Use it as soon as you pull, and keep it up at all times.
6). I then used my stun. Oh, I forgot to mention -- I'm a Beast Master. I don't know how this fight would go with any other spec, I'm not even sure if it is possible with another spec. But, I used my stun early in the fight, as it has (for me) a 42 second cooldown, which means I will likely be able to use it again later. The reason for this is two-fold: Not only does it prevent Tusker from getting out another 1-2 melees, it also gives Mend Pet a 1-2 tick lead on Tusker's damage. The whole battle is nothing but a Race between Mend Pet and Tusker's melee attacks. You're doomed to lose this race; your foe is faster than you. The only way you're going to win, is to DPS her down before she gets to the finish line.
7). Speaking of DPS, after Stun wears off, I immediately began casting Gift of the Naaru on my pet. Don't forget, you can cast it on your pet for Amazing Results. GotN and Mend Pet DO Stack, and that is what will save your brave and daring rear in this fight. As soon as GotN was casted, I then scrambled for all of my "kill this NOW!" buttons: Rapid Shot, Bestial Wrath (which also kicks in The Beast Within), Bladefist's Breadth (+attack power trinket), and I started spamming Arcane Shots.
8). Don't Forget about Mend Pet!!! Even if you "waste" Mana using an extra Mend Pet or two, wasting a few ticks, make SURE it is up AT ALL TIMES. 2-3 seconds without Mend Pet will kill your pet (and you soon afterwards). Continue with the Scorpid Stings, too. Don't let that go down either.
9). When your Stun is back up, use it ASAP! Pray that it gets in 2 ticks of Mend Pet.
10). Hopefully Tusker is either dead, or almost dead at this point. When I did it successfully, my pet died when Tusker had 1k HP left. She runs kinda slow; I got in 2 auto-shots for 300 each by the time she reached me, and I ran backwards. I was completely OOM, and was machinegun-tapping my Arcane Shot key, and I managed to blast her for 360 damage (55 overkill).
It was a very close and heart-pounding fight, but definitely a true test to any Draenei Hunter out there.
If another race manages to do this at Lv68 without being twinked out, I'd love to hear your testimonies. I did this in nothing but quest rewards, using Ironbite Shells, and a Knothide Ammo pouch. I had roughly 1,200 AP, and I think I had about 240 DPS on my ranged attacks without the Improved Aspect of the Hawk proc. Nothing fancy, but I still got the job done. Barely.