Greetings young Grasshoppers. So you've come seeking wisdom on how to solo raid bosses, eh?
Whether you're after some sweet transmog gear, chasing a new rare raid drop pet, looking for a mount that supposedly exists, or just in the market for a few luls, I am here to happily give you a few pointers on how anyone of any class (and *most* specs) may do any of the things mentioned above.
Pull up a chair and let's get down to my top 5 tips on soloing old content.
1. Throw your old raiding habits out the window
For DPS: You know those old time rules that are practically beat into the head of any raider ever? That silly thing called "watching your threat" and "not standing in front of the big baddy"? Guess what, both of those ideas need to go. No more hiding behind the skirts of some tank. YOU are now the tank. You need to THINK like a tank, move like a tank, DODGE ALL THE THINGS like a tank. You know how you'd maybe only hit those personal defensive cooldowns when the raid damage got kind of ouchie? Yeah, you'll have to learn where you'll actually need to preemptively hit those for certain fights during times you may not be used to. Those security of life blankets we know as healers? GONE. You, my dear little one, are now your own healer. You'll have to learn how to time your personal healing cooldowns to keep yourself from becoming a crispy corpse on the floor.
For Tanks: You dudes and dudettes pretty much do what your usually do, but now it's with a bit of a twist. You'll now be up against possible enrage timers that you'll have to play the role of DPS to get past (though, you buggers with your Vengeances, for the most part damage dealing shouldn't be much of a problem). Like the DPS though, you know longer have your healers at your back. You'll have to absolutely know when to use your mitigation cooldowns to prevent your health from dropping in the first place, and you'll have to know how to heal your own hide in the event that it does dip in percentage.
For Healers: First of all if you're soloing things as a healer, you are A) bloody insane and B) a badass if you're actually pulling it off. In general, with the exception of perhaps Discipline Priests and maaaaaaybe Restoration Druids specced into Heart of the Wild, most healers these days don't have a whole pile of consistent hurt to put out there. Likewise, the majority of healers lack enough personal defense cooldowns to rotate through a given fight. Some do, some don't; the mileage may vary. What I'm getting at is that soloing as someone in a healing specialization may not necessarily get the best results due to either enrage timers or hard hitting mechanics. I shall not deter you from your goals though. If you wish to solo content as a healing type, you go out there and get on with your fancy self.
2. Be aware of EVERYTHING
To semi-contradict the title of the previous point I made, not all raiding habits should be thrown out of the window. Certain things such as getting out of the fire as quickly as possible and watching your timers? Great habits to hold on to. While yes, there are many encounters where the mechanics can now pretty much be ignored, there are still plenty of situations where you'll want to avoid the bad, damage x component of y boss at z time, take down adds so that they don't nuke you, burn down that boss before he can push you six feet under, heal at this time, move when that happens, etc. This goes double for you if you're going for achievements, since many of those are "Don't get hit by this!" or "Kill x of that!" You'll need to watch your feet, your health, the boss' positioning, buffs/debuffs, possibly dispells, interrupts...all the things that you'd usually have 9 or 24 other brains and sets of hands helping you take care of, all by yourself.
It's as if your raid awareness suddenly needs to be hopped up on coffee. The special kind.
3. Know thine utility
Unless you're a high(er) end PvP type, or on the cutting edge of PvE content, changes are pretty good that you may only be aware of a small fraction of the toolkit available to you. It personally took me many years to learn fully understand how important it was to use Shamanistic Rage as a defense cooldown (heck, for a while in ICC it was a DPS cooldown of all things...). With the added utility that has been added into Mists of Pandaria, I'll even admit that there are times when I forget to use certain totems in certain situations (Capacitor Totem is notoriously forgotten by many shaman, yours truly included sometimes). Soloing content will often force you to think outside the box as far as your cooldowns and bag of tricks are concerned. Dismiss nothing in your toolkit. Become familiar with how certain cooldowns may interact with each other, if you're not already. Test out which utility spells help you out in which situation. Push your limits, your knowledge, and if you seem to be falling short, start digging to learn more. Never stop playing mad scientist.
4. Know the fight
Yes, this might be a /facepalm tip but it really does pay to know the mechanics of a fight, even if most of those mechanics no longer necessarily apply. If you cannot kill something within your "zerg" window, you may find yourself having to play nice with mechanics. You may have to roll defensive CDs to mitigate Patchwerks Hateful Strikes. You're going to have to be aware that all three body parts of Mimiron will need to die within a certain time frame from each other in the final phase or things on him will gain health back. And of course, if you're an achievement chaser, you absolutely will need to know how both the achievement works and the mechanics of the boss. A little knowledge can go a long way in preventing frustrations and achievement failure.
5. Know your limits
Soloing is part character level, part gear, part skill, and sometimes even part luck. Some raids are easier to solo once you hit x level plateau. Some boss mechanics are impossible to deal with until you manage to hit y gearing threshold. Many fights have RNG aspects to them that may frustrate you. All of these aspects can affect you to varying degrees depending on your skill level on any given character; some encounters may be neigh on impossible for you until another aspect of the presented equation shifts. It is my firm belief that if you want to solo something, give it a couple of shots. Try anything once, if only for the laughs. If you manage to down it, great! If not, know when it's time to leave it be until you manage to get your mits on better gear or you familiarize yourself with your chosen class/spec further. Not all classes or specs can solo all of the things at the same time. A Blood DK can solo certain content much sooner than an Enhancement Shaman. An Enhancer can solo a lot more currently than say, a Holy Priest. Test the limits of your chosen role, but don't push yourself to the point where you hate what you're doing. Know your personal limits and the limits of your class.
Overall, taking on old content by one's own self is a bit like spinning plates. You need to be aware of a lot of things at once, and if you muck up the balance on one of the plates, everything may come tumbling down. It's all on you and you alone. It can be a bit overwhelming at first, but I think that's the beauty of it, personally. There's no blaming Cindy for missing her taunt, can't complain to Bob for not getting his heal off in time, and Jackie can't be yelled at for not DPSing hard enough. It's all you.
Soloing is a testament to your skill, patience, and I personally think that it shows a certain sort of dedication to your chosen character. It's not always easy, nor is it always pretty. It may come more naturally to some than it does to others, and that's perfectly okay. When you're soloing, you're not on anyone's schedule. No one but you can get frustrated at your mistakes or get huffy when you want to AFK for 30 minutes to grab a bite to eat or get the kids to bed. No one will ever breathe down your neck for not making enough progress in your allotted window. You take everything on in your own time, at your own pace.
One final tip I can give and cannot stress enough is this: Have fun with it. Try to view soloing not as some chore that needs to be done for x item, but as an opportunity to learn a few things about yourself as a player. You may find that you have certain strengths and weaknesses that you weren't aware of before. Soloing is an excellent time to work out some kinks in your playstyle, not to mention to have a little bit of in game *you* time. Again, have fun with it and roll with the punches. Now get out there and do your thang.