[3.10] Wallach's Hierophant Holy Flame Totems (Full Simulacrum Clear)

Primary damage links in order of priority:

Holy Flame Totem -> Elemental Focus -> Fire Penetration -> Infused Channelling -> Controlled Destruction -> Added Fire Damage

Pretty straightforward, these are the highest damage supports you can link to your Holy Flame Totem. Infused Channelling claims to not apply its Infusion buff effect to totems (even though visually it shows them gaining Infusion for some reason), but even without Infusion the 39% more damage multiplier does work for totems, which is a larger damage increase than any of our other supports except for Elemental Focus.

Once you have more than 20% Physical as Extra Fire Damage on your gear (i.e. affixes on both your weapon and your amulet), you will find that Added Fire Damage value falls to where Combustion is the better support gem. You can see this for yourself in the example Path of Building link; until you have such gear, though, stick with Added Fire Damage support.

Offensive support 4-link:

Flammability -> Arcane Surge -> Increased Duration -> Spell Cascade

This should be your priority for your first spare 4-link. Remember to level your Arcane Surge gem such that the mana cost of Flammability is equal or higher than the trigger for Arcane Surge to grant its buff effect. You want Flammability to grant Arcane Surge every single time it is cast; maximum uptime is worth more than slightly increasing Arcane Surge's buff effect. Spell Cascade allows you to both increase Flammability's cost (to give you more room for a higher level Arcane Surge) and allows you to blanket a much larger area without increasing Flammability's cast time.

The reason this gem link does not contain Faster Casting is that it is intended to be socketed into Shaper gloves that contain the affix "Socketed Gems are supported by level 18/20 Faster Casting" on them. Until you have such gloves, feel free to drop Increased Duration for Faster Casting.

For late-game purposes, Projectile Weakness will actually prove to be a stronger curse damage-wise than Flammability, with two caveats; a much lower mana cost (making it harder to consistently trigger high-rank Arcane Surge) and a very high Dexterity requirement (155 Dexterity required for rank 20). As such, I recommend you stick with Flammability from the outset and only in endgame once you have the flexibility and currency to start refining gear for minor stats like +Dexterity, consider switching to Projectile Weakness. Just remember to keep an eye on your rank of Arcane Surge; you generally want to trigger that buff within 2 casts of your curse so that you are never without the Arcane Surge buff. Personally, I plan to just stick with Flammability.

Offensive support 4-link:

Wave of Conviction -> Spell Totem -> Multiple Totems -> Combustion

This 4-link will allow us to summon an additonal pair of totems (beyond our normal Holy Flame Totem limit) that will repeatedly cast Wave of Conviction, applying both -25% Fire Resist through Fire Exposure, as well as -19% Fire Resistance when an enemy is ignited thanks to Combustion. Furthermore, the additional 2 totems will boost the effects of our Ritual of Awakening ascendancy notable, further increasing our damage and life/mana regeneration. These totems will also not be trivial in terms of added DPS on single targets just through their own hits.

Utility support 4-link:

Steelskin -> Cast When Damage Taken -> Increased Duration -> (Your Choice)

I've actually started running Steelskin over Immortal call as of late; even though we do generate Endurance Charges in this build, we have a low base amount of physical mitigation, and do not rebuild our Endurance Charges that consistently after Immortal Call eats them, which can leave us a bit vulnerable to physical damage once Immortal Call wears off if we are not fully out of danger. Steelskin doesn't consume our Endurance Charges when it triggers, so we get to keep the additional physical mitigation at all times. The downside of Steelskin is that it requires a much higher rank of skill gem to really be useful later, so you'll want to level up Steelskin and Cast When Damage Taken to relatively high levels. I personally run a level 17 Cast When Damage Taken and a level 19 Steelskin, which allows Steelskin to absorb up to around 2k damage during its buff effect.

The final link here is yours to decide; Vaal Righteous Fire would be my recommendation as it is a big damage increase when available. Just make sure whatever you slot here is high enough rank that it is not triggered autoamatically by Cast When Damage Taken unless you want it to be.

Movement links:

Flame Dash -> Second Wind -> Portal

Flame Dash's cooldown recovery rate was nerfed in 3.10, so we want the new Second Wind support to add an additional charge to Flame Dash's count, as well as provide some additional cooldown recovery rate to help offset the loss in recharge rate. Portal here can be replaced with whatever you prefer, I just like not being tied to Portal Scrolls.

Essence Worm ring sockets:

Herald of Ash

Even though Herald of Ash is not considered an Aura gem and thus does not gain the +2 levels from Essence Worm, a level 20 Herald of Ash still increases our damage significantly more than a level 22 Anger, so Herald of Ash takes priority.

Pursuit of Faith -> Ritual of Awakening -> Conviction of Power -> Divine Guidance

Not much choice here for a totem build. Luckily all four of these nodes are very strong and make Hierophant the standard bearer for totem builds.

Doom Cast - Since we aren't pathing to this part of the tree, anointing Doom Cast will net you a ton of damage through increased critical strike chance with a side of critical strike multiplier. An expensive option but hard to beat in terms of raw damage. Note that if you significantly increase your base critical strike chance (such as through the expensive Bottled Faith flask effect), the value of this will drop to where you will be better off anointing something like Heartseeker below for pure critical strike multiplier.

Heartseeker - This notable grants the exact same bonus of 30% increased critical strike multiplier as Throatseeker, but at a much lower cost due to cheaper oils, and is a strong damage gain for our build.

Soul of Steel - This is probably our premiere defensive notable option. The armor and physical damage reduction really help with our biggest defensive weakness of physical damage, and the +1% to maximum elemental resistances works out to about a 4% reduction in elemental damage taken. It also won't require any adjustment to your life or mana pools in terms of maintaining your Mind Over Matter ratio to get full effect.

Constitution - This is another great defensive choice that grants the single largest life increase of any notable on the passive tree. The only real downside is that it may require you to shuffle some investment around to ensure you can cover the additional life with Mind Over Matter, but we are connected to plenty of good mana nodes in the passive tree if that is needed.

Note: These flasks are just general recommendations, feel free to swap or experiment with other flasks to suit your needs.

Bubbling Divine Life Flask of Staunching - Your first flask slot should generally be a life flask to help heal back from any big hits you might take. The ideal suffix here is Staunching so that you have the ability to remove dangerous bleed effects (such as the heavy bleeds put on you by Labyrinth spike traps) on demand. I personally recommend a Bubbling Divine Life Flask of Staunching, which will reduce the overall amount healed but grant some instant healing to help counter spike damage. Some folks prefer Seething prefix for purely instant healing at an even slightly lower value. Use whatever you're comfortable with here so long as it has the Staunching suffix for the bleed removal.

Wise Oak Bismuth Flask - This unique flask will grant us up to 15% Fire Penetration so long as our Fire Resistance is the highest of our three elemental resists. It will also grant some additional damage mitigation against whatever elemental damage type we have the lowest resist of. While quite difficult to do, if you can get all three of your Fire, Cold, and Lightning resists to the exact same number, you will get both of the flask's effect in all three elements (since all three resists will technically be both your lowest and highest elemental resists). Worth doing as a very endgame point of min-maxing, but for the most part you should be concerned only with ensuring your Fire Resistance is highest so that you get the Fire Penetration effect from this flask.

Chemist's Diamond Flask of Heat - Our most vital damage flask, as making your critical strike chance "Lucky" means it rolls twice to attempt to score a critical strike with every hit. This is also a good place for your Heat suffix to allow you a way to escape from being Frozen; you don't want to open any magic or rare strongboxes if you don't have a Heat flask handy, or they can be guaranteed death if they Freeze you upon opening. Chemist's prefix here gives us 2 uses from full charges with 10 charges left over, meaning you will get a 3rd use almost immediately.

Chemist's Silver Flask of Grounding - Another good damage flask that also grants movement speed. We take Grounding here since Shock can be a pretty dangerous debuff in harder content, so its nice to have access to Shock immunity. Chemist's affix will grant us 2 uses from full charges.

Chemist's Quicksilver Flask of Warding - This isn't the fastest build around, so a Quicksilver flask is great for improving your mapping speed and general quality of life. Warding suffix will grant us more consistent protection against curses; while you can just run through your Holy Flame Totem to clear most monster-sourced curses, maps that have permanent curse debuffs can be pretty obnoxious to deal with when you don't have the regular uptime of a flask to keep them off you (particularly Temporal Chains).

Feel free to swap the immunity suffixes on the utility flasks above around as needed. If you want to cover ignite removal / immunity as well, you'll probably want to drop the Wise Oak flask to something like a Granite Flask of Dousing, or have a spare one of the above utility flasks with Dousing you can swap into for maps where you know you might need it (such as dealing with the Enslaver Elder Guardian boss).

(Major) Soul of the Brine King - We don't get any stun immunity in this build, so Brine King helps prevent us from getting totally stunlocked in bad situations. The reduced Chill effect is also good for fights like Uber Elder where your Freeze flask can run out leaving you very vulnerable to Chill.

(Minor) Soul of Shakari - Honestly the Minor doesn't make too much of a difference in this build. I often leave Shakari on for the Poison immunity (once upgraded). Especially useful to be immune to the poison from dart traps in the Labyrinth. In the end, though, just use whatever you're most comfortable with here.

Help Alira (5 Mana Regenerated per second, +20% to Global Critical Strike Multiplier, +15% to all Elemental Resistances)

Especially as a league starter, helping Alira is simply too beneficial to this build to take over 2 passive skill points. The resists and mana regeneration are super useful at the start of the game and remain good bonuses all the way through Uber Elder, while critical strike multiplier is weak early but the strongest offensive stat available to us at endgame. At the high end of things you can only get slightly more damage out of 2 passive skill points; the sacrifice of resistances and mana regeneration simply isn't worth it in my opinion.