Low Life Barrier Invocation Comet Spam Infernalist

Atziri's Disdain [Poe2wiki] (can be replaced by mirror tier ES helmet if you're rich... I'm not)
Important stats:
#% of damage taken bypasses energy shield (as low as possible, ideally min-rolled)
Gain #% of maximum life as extra maximum energy shield (as high as possible, ideally max-rolled)

Ligurium Talisman [Poe2wiki]
Important stats:
None, but all are good. Just buy what you can afford.

Rise of the Phoenix [Poe2wiki]
Important stats:
None, but it's dirt cheap so just buy it max-rolled.

Coward's Legacy [Poe2wiki]
Important stats:
#% reduced flask charges used (as high as possible)
#% increased life and mana recovery from flasks (as high as possible)

Rare body armour
Important stats:
Energy shield (This and Atziri's Disdain are by far your largest sources of energy shield, so splurge a bit and make sure it's got a lot of energy shield)
#% reduced ignite duration on you (not required by any means, but the self damage ignites you quite frequently so this stat is better than you'd think)

Rare wand
Important stats:
+# to level of all (Cold) spell skills (This is a really effective way of raising the cost of Comet and it also improves its damage significantly)

The rest of the gear just needs to have lots of resists, enough attributes to meet requirements and as much life and energy shield as you can afford. Don't forget movement speed on boots.

Barrier Invocation
- Comet
- Spell Echo
- Capacitor
- Impetus
- Supercritical? (don't have a six-link yet so can't test)

Grim Feast
- Herbalism
- Vitality

Blink
- Ingenuity
- Second Wind

Eye of Winter
- Unleash
- Cold Exposure
- Inspiration
- Strip Away

Hypothermia
- Heightened Curse
- Cursed Ground
- Mobility
- Arcane Tempo

- Cast Hypothermia until you overflow your Infernal Flame whenever you enter an area.
- Activate Barrier Invocation once or twice per second to maintain recoup.
- Activate your life flask after every other activation of Barrier Invocation to maintain recovery.
- Mouse over any monsters you see to drop comets on them.
- Cast Eye of Winter on rares/uniques every so often to apply critical weakness and cold exposure.

Barrier Invocation gains 1 energy per 5 energy shield you lose from hit damage, up to a maximum of 500. Capacitor increases this maximum to 900. This means that we need to lose 900*5=4500 energy shield to hit damage in order to reach maximum energy. We do this with the self damage from Pyromantic Pact which is based on 100% of our max Life and energy shield and is dealt to us as fire damage. Rise of the Phoenix and Enhanced Barrier give a combined total of 6% maximum fire resistance so our cap is 81%. This means that we actually only take 19% of our maximum life and energy shield as fire damage. Atziri's Disdain makes 20% of this damage bypass our energy shield so the energy shield we lose is actually only 19*0.8=15.2%. On paper, this means that we need our life and energy shield to combine to a total of 4500/0.152=29606. Ouch... Luckily #% energy gain modifiers exist. Barrier Invocation gets 3% per level and 15% from quality, Impetus adds a further 40%, the tree has 55% and jewels can have up to 15%. Currently, my jewels give me a measly 24% and my level 16, 20% quality Barrier Invocation gives 60%. All of this totals to 179%, which lowers the life and energy shield requirement to 29606/2.79=10612. Still a lot, but with Beidat's Hand, Atziri's Disdain, and a decent Rare body armour, this is totally doable.

Still sane exile? There's still more math left, but don't worry, the hardest part is over. Now that Barrier Invocation caps out its energy every time we overflow our Infernal Flame, all there is left to do is make sure that happens every time we use it. The skill I've chosen to trigger is Comet which naturally has a very high mana (and therefore Infernal Flame) cost, but you can probably make this work with just about any spell in the game. Comet has a base cast time of 1 second and adds 1 second to total cast time (which counts double now), so it consumes (1+1*2)/0.1=300 energy on use which means we get to trigger it thrice per use of Barrier Invocation. To get our Infernal Flame to overflow exactly once per activation, we need to make sure that Comet's Infernal Flame cost is higher than a third of our maximum Infernal Flame, but lower than half of our maximum Infernal Flame. You can play with gem levels and mana modifiers to make sure this is the case. My level 17 Comet currently costs 379 Infernal Flame and my maximum is 1022. 379*2=758 < 1022 < 379*3=1137 so we're good there.

So now we can spam spells at the click of a button. Great, but we lose a large chunk of life and energy shield whenever we do so. to remedy the life loss, we need to get our life recoup to be somewhere above 20% so that the 20% bypass from Atziri's Disdain is covered. I do this with the passive skill tree, but you can get a lot of recoup from jewels as well. The energy shield situation is a bit more complicated. Energy shield recovery in PoE 2 is significantly more difficult than in PoE 1, which means we need to use every trick in the book to get our recovery to be decent. Every trick in the book means basically 2 tricks in this case; flasks and regeneration. Both of those apply to life by default but Eternal Youth makes our flasks apply to energy shield and Ligurium Talisman does the same for regeneration. to get the most out of both, we use Rise of the Phoenix in combination with Coward's Legacy and Desperate Times as an anoint on our amulet to have 7.5% of energy shield regenerated per second and 80% increased recovery from our life flask. Vitality and Herbalism raise this to 8.5% and 110% respectively. With a good life flask and the large amount of energy shield we have, this can easily lead to 2500 to 3000 energy shield recovered per second. More than enough to spam frequently without killing ourselves. As an added bonus, if we stop spamming, we're practically unkillable outside of one-shots.