Know your role
The first thing to understand about Arcanist is what you are actually capable of, which is a bit more complex than with some other classes. You're not a healer, but you do have the option to heal. You're not pure DPS compared to a Thaumaturge, but you can pump out some damage. No, your greatest strength lies in debuffing, debilitating, and generally swapping roles as necessary -- because you can do a lot of stuff.
Arcanists have a crapton of tools. By the time you've done the level 15 class quest, you have both a DPS summon and a tank summon, both of which can work quite well in the field with you. You have a heal that's every bit as potent as Cure, and while it takes a while, you eventually pick up both a Raise equivalent and a damage shield of sorts. You can pass several DoT effects around, preventing enemies from healing, slowing them, and reducing their damage output. And you've also got plenty of raw damage that's not linked to any elemental attribute.
What's your weakness? Well, you can do all these things... but you're kind of awful at all of them. Your direct damage spells don't have the punch of even the Blizzard line of spells for Thaumaturges. Your pets are survivable enough but not against high-end enemies, and when your pet drops, you feel the loss very acutely. Your heal is weaker than Cure simply because you pick up Enhanced Intelligence traits rather than Enhanced Mind. The one unique trick you've got is your debuffs, none of which lasts forever.
This means that even solo, you have to play smart. Playing correctly, you can be a force to be reckoned with in both solo and group content. Playing incorrectly, you'll wind up being a weaker Thaumaturge with a heal.
Ruin: The non-elemental Ruin line makes its appearance once again, and astute players will notice right away that it has a ridiculously low attack potency of 80. Compare that to most damage spells starting higher, and you'll swiftly realize that Ruin is there to fill out the spaces when you're not using more useful stuff.
Bio: Your first debuff, Bio, is an instant-cast spell that deals damage over time. That's it. That's all it does. It sounds pretty underwhelming, except it's a great way to layer on extra damage while only eating up a single GCD. It's crucial to keep Bio up if you're doing DPS, but even when healing, you can toss it on a boss at the start for a bit of extra bite.
Summon: Summers are sort of the entire point of the class; Arcanists had two summons available in beta. Emerald Carbuncle served as DPS, while Topaz Carbuncle served as a tank. (I would not be surprised to see a third Carbuncle serving as a healer, but that's speculation.) The summons are long and MP-heavy, so they're not something to be used in the midst of combat.
All pets can be commanded to do everything you'd want from a pet, including an order to attack without using special abilities unless you command otherwise. Worth noting is that Carby has no concept of retreat and will happily pursue fleeing invincible targets, such as one of the bosses in Sastasha, until he is out of range and despawns. Be ready to tell the little glowing guy to stay.
Miasma: A debuff with a cast time that deals both damage over time and weakens the target notably. On light targets you expect to die quickly, Miasma is a waste; on stronger targets, including most enemies you fight while soloing, Miasma is an opener and worth maintaining. DPS Arcanists will want it up on bosses. Note that the DoT lasts longer than the Bio DoT.
Physick: Standard single-target heal, indistinguishable from Cure in every way.
Aetherflow: Instantly restores 20% of your MP and grants you a stack of Aetherdam. On a one-minute cooldown. Aetherdam lasts forever until used, so it might be worth using Aetherflow early just to have Energy Drain on tap when needed. Between the two, you can keep going for quite some time.
Energy Drain: Instantly does damage, drains health from the target, and restores MP. Only usable with Aetherdam. In a pinch, you can use Aetherflow and then immediately hit Energy Drain for a quick one-two burst of restoration -- or save a 'dam early, then Energy Drain, Aetherflow, Energy Drain. The amount healed by the HP drain is not terribly substantial, but it restores reasonable amounts of MP.
Virus: A substantial debuff to physical attackers, reducing Strength and Dexterity by 15%. Magical attackers won't hurt from this, but it should be an obvious cast on bosses. Has a minute and a half recharge, which prevents constant use.
Tips for Arcanists
Your priorities on solo fights are pretty simple: pull with Miasma, hit Bio, then hit Ruin while your Carbuncle of choice does its thing. If you or Carby run low on health, bust out Physick. You won't find many targets that really require Virus, Aetherflow, or Energy Drain while out on your own unless you pull two things by accident. It's actually pretty easy to juggle two targets at once; wait until one is nearly dead, then let Carby and DoTs finish off the first target while you pull ahead and hopefully continue your EXP chain.
The Duty Finder will not allow you to queue up in the low levels as a healer, so as a DPS, grab some cross-class DoTs and focus on those damage ticks. You won't have the area output of a Thaumaturge, but you'll sustain longer in a boss fight. However, if you have friends willing to try it, you can heal through one of the early dungeons as an Arcanist. You'll need a backup healer (another Arcanist or a Thaumaturge with Cure/Physick) and will want to cross-slot Protect, but it is doable.
Try to figure out what you want to do in the later game fairly early on. Obviously putting most of your stat points toward Mind will mark you as a Scholar, while putting them toward Intelligence marks you as a Summoner. A 15/15 split is certainly acceptable, since you have tools to make up for lower MP by avoiding Piety.
Always remember to shift your pet based on content. Some bits of content, especially some story missions, provide NPCs who serve perfectly well as tanks. Others have NPCs who serve perfectly well as healers. Know what you're facing and be ready to shift at a moment's notice. This goes for the class as a whole, at that -- you can be doing DPS one moment and shift to healing for a bit if it's necessary. Think, analyze, and change according to the situation.
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