This is not a guide. These are my opinions based on what I've seen from videos alone, and I posted it because I'd like to see what other people's opinions are. I'd greatly appreciate if people didn't make proclaimations about my ignorance/intelligence if their opinion differs from mine. I'd prefer they just shared their reasons for why their opinion differed.
Firstly, just a point about Gloves vs Boots on single target. Both Boots+2pcT19+4PcT20 and Gloves+4pcT20 sim almost identical to each other according to both Effinhunter's sims and Azortharion's sims. However, there are two factors I think will favour the Gloves:
1. The Gloves allow 50% of your Aimed Shots to be cast while moving. This is not factored in the sims, and definitely has a positive impact on DPS, potentially significant (depending on how well you play with the gloves).
2. The sims (at least in Effinhunter's sims, since he's the only one who provided the simcraft source) were done using T19 having the same ilvl as ToS gear, when in reality your T19 gear is likely to be lower (purely due to simple statistics: gear from ToS drops at a higher baseline ilvl than T19, therefore will have a higher ilvl on average). This means the 2pcT19+4PcT20 sims are likely overestimating the benefit that most people will get from it, although the extent of overestimation would of course depend on how lucky you got with T19.
For these reasons, I conclude that the Gloves+4pcT20 are superior to Boots+2pcT19+4pcT20 for single target. However, it might be worth using the Boots instead of the Gloves for single target initially since you'd probably want to upgrade the Boots first (I explain this later).
Note: Every time the Gloves are used, the assumption is just 4pcT20, everywhere else you would use 2pcT19+4pcT20. Mainly because if you're not using the Gloves, that means it's an AoE/cleave fight (Trueshot is a powerful AoE/cleave cooldown, making 2pcT19 more powerful on these fights).
Goroth
Legendaries: Ring/Gloves
Talents: True Aim/Patient Sniper/Crows/Trick Shot
Reasons:
This appears to be a pure single target fight.
Demonic Inquisition
Legendaries: Boots/Gloves
Talents: Lock n Load/Patient Sniper/Crows/Trick Shot
Reasons:
This one I'm not sure about. There are some phases where the two bosses must be tanked apart (which would favour a single target setup), and then there are some phases where they can be tanked together (which would favour cleave setups). Whether a pure single target setup or a cleave setup is better would depend on how often the bosses can be kept together.
Update: When I did the fight with my guild, the bosses were kept apart the entire time so there was no opportunity to cleave at all. If this is the optimum strategy then this fight is essentially entirely single target. However, you do still have to target switch between the bosses very often (as well as enter the chamber to remove torment) which means True Aim is probably not optimum (making the Ring useless). The only good single target legendaries left would be Boots/Gloves.
It's possible that True Aim might still be good (since you can stick to one boss most of the time if you time it right), in which case Ring/Gloves would be the best.
Harjatan
Legendaries: Boots/Belt
Talents: Lock n Load/Explosive Shot/Volley/Trick Shot
Reasons:
There are constant add spawns, which favour the burst AoE build of Explosive Shot/Piercing Shot.
Update: When I did this fight with my guild it seemed like the adds fixated on random players, so they never really clumped up enough to be cleaved effectively so I've chosen to use Trick Shot instead of Piercing Shot here (to maximise damage on the specific add you're going after, as well as the boss).
Mistress Sassz'ine
Legendaries: Boots/Belt
Talents: Lock n Load/Explosive Shot/Volley/Piercing Shot
Reasons:
There are constant add spawns that seem to clump together, which favour Explosive Shot/Piercing Shot.
Sisters of the Moon
Legendaries: Ring/Gloves
Talents: True Aim/Patient Sniper/Crows/Trick Shot
Reasons:
There are multiple bosses, but you'll only face one at a time as far as I can see. This means a single target setup should work best.
The Desolate Host
Legendaries: Boots/Belt
Talents: Lock n Load/Patient Sniper/Volley/Trick Shot
Reasons:
It looks like you'll almost always have some adds up, but a lot of them will be almost immune to damage, so you can't just AoE them all down, which means Explosive Shot/Piercing Shot will lose some value. However, this plays right into the benefit of the belt, which allows you to funnel your AoE damage into single target Aimed Shot damage, allowing you to choose which target the damage is going to. Trick Shot also means your Aimed Shots will still be doing good AoE damage too though, with the ricochets, but you won't be able to use True Aim because of this.
Maiden of Vigilance
Legendaries: Ring/Gloves
Talents: True Aim/Patient Sniper/Crows/Trick Shot
Reasons:
Pure single target fight.
Fallen Avatar
Legendaries: Ring/Gloves
Talents: True Aim/Patient Sniper/Crows/Trick Shot
Reasons:
Mostly pure single target fight. There is an add that stays alive for a very long time, but you don't want to damage the add until it gains the absorb shield, in which case you'd want to single target it down.
It might be possible to argue that the Boots/Gloves or Boots/Ring are the better choice if you are unable to get Trueshot to come off cooldown for each absorb shield phase (since these are a DPS race of sorts). But then again, the last phase is pure single target and is also a DPS race, which would favour Ring/Gloves. It just depends on what your group is having trouble with (removing the absorb shield in time, or killing the boss in time), although I'm guessing removing the absorb shield is a job hunters would be given.
Kil'jaeden
Legendaries: Boots/Gloves
Talents: Lock n Load/Patient Sniper/Crows/Trick Shot
Reasons:
This seems to be a mostly single target fight. There are lots of adds, but they are always far apart so you never get to cleave them (ruling out Explosive/Piercing Shot). Kil'Jaeden also periodically becomes immune to damage, so (along with the constant adds which you have to switch to), True Aim doesn't seem viable as you'd constantly lose the stacks (thus the Ring would not be a viable legendary either).
Summary
There are only four legendaries used. They are:
1. Gloves on 6 bosses.
2. Boots on 5 bosses.
3. Ring on 4 bosses.
4. Belt on 3 bosses.
(Total is 18 since you use 2 legendaries per boss)
However, if you upgrade the Boots first, you can reasonably use them for single target instead of the Gloves, which results in the Boots being used for every single fight (while the Gloves would only be used on two fights: Kil'jaeden and Demonic Inquisition). This means the ideal order to upgrade the legendaries would appear to be:
1. Boots
2. Ring
3. Belt
4. Gloves
One important point to make would be that in order for Boots+2pcT19+4pcT20 to be better than Gloves+4pcT20 on single target, you'd need to have two decent T19 pieces. If you don't, then you'd want to upgrade the Gloves second (after the Boots), since you'd still want to use the Gloves for 5/9 fights, even after you've upgraded the Boots. You'd also probably upgrade the Gloves second if you were interested in your DPS on Kil'Jaeden (since it'd be logical to assume that this is the hardest boss).
Another point might be that you could end up taking a while to get 4 pieces of T20. This means you'd be stuck with 4pcT19+2pcT20 when using the Boots or 2pcT19+2pcT20 when using the Gloves (since 2pcT20 is much better than 4pcT19, especially when used with the Gloves). This should make the Boots more powerful relative to the Gloves (compared to when using 4pcT20), since the 4pcT19 makes Trueshot more powerful, which in turn benefits the Boots. In other words, this point doesn't really change anything, it just gives even more of a reason to upgrade the Boots first.
Regarding Belt vs Ring: The Belt is much better itemised than the Ring (which is actually significantly underbudgeted for it's ilvl) which means you'll gain significantly more stats when you upgrade the Belt than when you upgrade the Ring, so it could be better to upgrade the Belt first, although you'd never use the Belt at the same time you were using the Ring.
So these are my opinions. Does anyone have their own opinion? Have I understood the mechanics of each boss accurately? Perhaps one of the other 8 legendaries could have some quirk that makes them useful in a particular fight?