Truthfully, soloing chess is partly a matter of luck, in no small part because Medivh adores cheating. You may beat it the first time, or (more likely) suffer through a maddening series of losses until the stars align and you get the "kill." The one consolation is that you won't have to run back from the graveyard; you can't die on Chess, and within a few moments following a loss (or win, for that matter), the board will reset and you can try again.
Trash clear: All stealthable, but if you'd rather kill things , budget a good 10 minutes or so. Fortunately for your groaning bags, the ethereal trader Ythyar is right outside the entrance to the game room.
Kill: It takes me about 6-8 minutes to clear Chess if things go well.
Gear: n/a. How hard?: Eh. This is one of those things where you'll get a quick kill and wonder what the big deal is, or still be there 25 attempts later restraining yourself from having a psychotic episode. The best bit of advice I can give you is to move your pawns up a space or two so you can move your king/queen out of the fire that Medivh will almost certainly spawn beneath them. Get your "queen" (i.e. the conjuror for Alliance, warlock for Horde) DPSing on the opposing king as quickly as possible, and keep this piece safe; they do a lot of damage, and more importantly, they can do it from range. With luck, Medivh will be dumb enough to move his king within range of several of your pieces, and you should dogpile him if/when this happens. If you've got enough of your own pieces on the enemy king, you should be able to DPS through any heals he's getting from the enemy priests.
Bladed Shoulderpads of the Merciless: If I recall correctly, these were the only non-set melee leather shoulders in tier 4, and by God did they suck for druids. I couldn't get Ikiss to drop the Shoulderpads of Assassination, and I wasn't then part of a raiding guild (so tier 4 shoulders from High King Maulgar were out of the question), and I wound up using these until I'd suffered through enough arena for season 2 shoulders. I hated arena and vowed never to set foot back inside, until I realized (after being accepted to a raiding guild) that no sane raid leader wanted to do pre-nerf Magtheridon or pre-nerf Kael'thas more than they absolutely had to. Can you guess what those bosses dropped? Yep, that would be tier chests...with yours truly still in heavy clefthoof on the cusp of tier 6 content. Hello again, arena!
Girdle of Treachery: By contrast, this was actually a really nice cat piece. I think the quest reward Manimal's Cinch still outclassed it for bears, but keep in mind that this was in the era of bonus armor, which Manimal's had in spades. Oh, BC feral itemization...never come back, please.
Sorry, folks, I don't have any tips for you here. I didn't actually believe Netherspite could be solo'd up until recently, when I found a few videos from players who attempted it as Wrath progressed (one's included above and is, happily enough, from the perspective of a feral druid). Death knights were able to solo it in early 2009 by popping some overpowered cooldowns and/or kiting Netherspite out of LOS of his portals, but Blizzard's nerfed their cooldowns and leashed Netherspite to his room as well. I shrugged it off and (incorrectly) figured Netherspite would remain among the ranks of bosses impossible to solo.
I'll be trying this next week when I get a chance, but until then, your guess is as good as mine as to the quality of the gear it requires. The player above seems to be in a mix of tier 7 and 8 with a Journey's End, and managed the kill in about a minute and 45 seconds, which works out to roughly 7.5K DPS without any buffs but Mark up. Before you respond, "Wtf hax!", he/she is also in the blue beam (which massively increases damage done) for most of the encounter, which is why you start seeing some truly stupendous numbers as the fight progresses. I'll give this a whirl and report back next Tuesday.
On your way up, you should take some time to see Medivh's bedroom and terrace, which is just off the spiral staircase. Exploring the non-boss-related portions of Kara is one of the things I never really got to do while clearing it with an actual raid, and there's some truly neat stuff off the beaten track. Soloing Kara is worth it if for no other reason than that. Trash clear: The Greater Fleshbeasts between yourself and Prince have Truesight, so you'll have to kill them. Be forewarned that they still hit respectably hard at 80, so don't run around pulling too many. If you head straight to Prince, budget around 5-6 minutes for the full clear.
Kill: About 6-7 minutes depending on infernal placement and gear quality.
Gear: Bear. You will need the survivability and health pool to outlast Prince's damage.
How hard?: As with Moroes and Oz, your chance of success here has an awful lot to do with the quality of your gear, and this isn't the sort of thing I'd advise trying in blues. Pull Prince to a wall (any wall, won't really matter which because you don't have a raid to worry about), and start DPSing the motherloving snot out of him. During phase 1, he really doesn't hit very hard, but his damage ratchets up in phases 2 and 3. Berserk off the pull, then again on cooldown. Parcel your defensive cooldowns out carefully, particularly Frenzied Regeneration. In general, you will see better survivability returns here from using two avoidance trinkets and a more avoidance-oriented tank set (if you have it) than you will with a stamina-heavy set due to Prince's swing speed in phase 2. This encounter (and others like it) was among the reasons that tanks were generally better about prioritizing avoidance in BC than they are in Wrath.
Even in ToGC/ICC gear with about 45K unbuffed health, it's not unusual for me to finish a solo Prince kill between 20-30%, and there's a bit of luck with respect to infernal placement. If you do wind up having to run around a lot to avoid them, try not to lose your Lacerate stack while doing so. Other than that, just keep to the bear's single-target rotation, keep Demoralizing Roar up, and hope you kill him before he kills you.
One more tip: if you get dangerously low, it's possible -- though risky -- to angle yourself out from a wall and eat the knockback from Shadow Nova. If you're fast, you can pop into caster, toss a fast heal, and pop back into bear before Prince catches up to you. Your timing has to be absolutely perfect, however, and you can't be playing with any serious latency. And, although this probably goes without saying, do try to make sure you're not going to be knocked back into an infernal. Notable drops:
Helm of the Fallen Defender: The Malorne tier helm, and a very pretty tier helm it was. I must admit that I am increasingly nostalgic over the BC tier sets in this, the age of the venus flytrap.
Nathrezim Mindblade: Coveted by balance players everywhere, and I desperately wanted one for my own balance set. However, the Mindblade -- along with Pillar of Ferocity off Anetheron in Hyjal -- eludes me to this day. I saw a few of them in BC but never once won a roll, but Pillar I have not seen at all.
Light's Justice: The best resto 1H-weapon from Kara, though less graphically interesting than its counterpart, the enormous Shard of the Virtuous off Maiden. I looooooved how a Shard looked on a male tauren.