Also, despite the Shadowlands class changes and level squish, the majority of these raids are still quite solo-able, with a few notable exceptions. It depends on the class you play and spec, you may be better at soloing but at least until Tomb of Sargeras I'd suggest that there's nothing that you cannot take on solo during Legion raids.
However before I pack my desk, which is a metaphor for my office, and depart I'd like to inform you that it's never as simple as just walking into a room and completing everything. There are some fights that are difficult for players to take on due to mechanics or outgoing damage can still be extremely high or both. Much depends on the class you play and spec and, most importantly, how much work and energy you're willing to commit in the event that you're looking for a simple run where you simply stomp things on the ground, Legion raids may still be a bit out of this category, but the higher your ilevel the more flexible they can be.
9.0.1 patch 9.0.1 brought in the level squish feature, and it could have an impact on what you can and can't do however it's not as extreme as I'd feared I've made it until ToS and have done pretty well. It might be a good idea to take a buddy or two to Antorus or the Burning Throne, if you're in search of mog gear prior to Shadowlands drops.
When you set out to be on your own
Certain specs are better at soloing than others. Tank specs, specifically those that have a high percentage of on-demand mitigation, self-healing or strong burst DPS, are very strong for soloing, as are DPS specifications that can provide an effective heal or absorb some damage as needed. You can also alter your Azerite abilities to increase their damage mitigation -- Gemhide is a good example, as does Resounding Protection -- but if are a holy priest you may have to consider changing towards Shadow or Disc for some fights. It's different on a case-by case basis. The most crucial piece of advice I can give you, particularly if this is your first time doing this particular content before for any reason, please look up the rules. A fight may demand an immense amount of DPS, or some serious mitigation to survive an entire phase. You need to know that going into. Kil'jaeden is a tough fight, and you can't just ignore what he dishes out. This is the case even in the period prior to Shadowlands, up to level 50. it will likely become easier when we're all around level 60.
The first thing to remember while running these raids is that they have various difficulty levels that are available for you. All Legion raids come with LFR, Normal, Heroic, and Mythic challenges, and you'll be able to run the four in a week, so if there's a specific appearance of gear that you're after that happens to be shared among them Keep that in mind. The majority of the time, though, gear can be quite variedfor instance, the Mythic appearance of an item of gear can differ, with added colors and even extra dimension to the item's appearance. For example, the class sets dropped out of the Tomb of Sargeras look very different on Mythic as well, so if you're trying to get the more limited styles, you'll need restrict yourself to Heroic or Normal.
The mechanics of fighting can be a challenge
One particularly annoying fight is Odyn who is fighting in the Trial of Valor raid. The raid opens and you'll encounter Hymdall and Hyrja who are both wearing this painful damage shield that they have when standing close together. Because you're on your own, they stand right over each other, and the only way to keep them from each other is to be patient until one begins to cast their large annoying spell. Then, use every ability that covers a lot of distance to reach to the other side of the room in order to cause some damage and possibly take out one of them before the other finishes casting and runs back over. It's painful when this doesn't work, and you are locked into the initial phase of the battle. This fight is soloable -I've tried it myself -however, if you are unable to manage to keep the two away long enough to finish either one down, it could be quite painful. Odyn himself is less difficult than his two-person warm-up acts. In both Emerald Nightmare and Nighthold are relatively easy to solo although some fights can be somewhat difficult but not overly difficult.
The truth is that any fight with weird mechanics can be a challenge to solo. The Demonic Inquisition encounter in Tomb of Sargeras is a good one to solo, after you've got used to handling it with the Unbearable Torment and knowing when to Confess, it's not really that difficult, though it does have a process of learning and you'll not likely be able steamroll them dead prior to it being played but. Another boss that I've had difficulty with -- in that I've not yet mastered it has been Aggramar in Aggramar in the Antorus raid. I know of people who have completed it and I'm sure it's possible however I've not yet accomplished it yet. I managed it with two buddies, but that's my personal best from my Arms and Fury Warriors -- I'm working on gearing up a Prot Set to give it an attempt that is more reliable in the near future.
For instance you're trying to complete the Balance of Power questline? It's not just solo-able and has been solo-playable throughout Battle for Azeroth -- Nighthold includes a few battles that are a bit challenging but you can pretty easily finish the raids each week. Gul'dan himself is not very difficult to take on for the majority of classes, particularly once you're at ilevel 66 or higher. By the time you're at or near to the standard Ny'alotha gear, it's quite easy to conquer. This is, prior to the time of Shadowlands. You can absolutely do Balance of Power right now.
Those little details still matter
Additionally, and this is a bit embarrassing, but ensure that you reach the raids. Argus requires you to open an quest chain, and if you haven't already completed that quest then you'll have to before you can get to the gate of Antorus. My Lighforged has found that out the hard way. If you'd like to move to LFR difficulties It's not as simple as going to the game and set it to LFR difficulty like you would use for Normal, Heroic and Mythic -- you must locate Archmage Timear in Legion's version Dalaran like the one above. He'll direct you to the wing of whatever LFR you'd like to go to.
So yeah, if you've wanted to dive into Legion raids for some time regardless of whether they're offering Legacy Loot now, or to complete old quests or achievements like Balance of Power, it's possible. Consider how difficult it was to play Hellfire Citadel at the end of Legion and you're in the same range of difficulty. It's tough enough that you won't an easy sleepwalk, but certainly within your abilities. There are some Antorus battles are more enjoyable with a few friends -- I'd prefer to have a small group of players to fight Mythic Antorus or Tomb of Sargeras. But doable. Definitely go ahead and try dipping your toes into.