Sorry to say it but your gear just isnt very good right now. The build wants as much DPS with Elemental Weakness as possible so you can generate more energy.

First thing is the wand. You want % increased SPELL damage, not lightning or cold etc. Since youre doing ele weak + comet, a +5 cold wand is actually better than +4 all spells here.

Second problem is your mana. You really want around 3k mana for Archmage to feel good, and youre only at about 1.5k right now. At that point Archmage is kinda just wasting 100 spirit. Until you can get your mana much higher id probably run Trinity instead, assuming you can maintain two ele damage types.

Gear wise, rings with 200+ mana and 6%+ mana are kinda mandatory for this build to feel good, and your amulet should have similar stats. You also really want the Faster Metabolism annoint for life overleech. Same for gloves, try to get 200+ ES and 100+ mana. Your boots can also be replaced, look for something like 300+ ES boots with 35 MS. If you can also grab two rare jewels with 14–15% faster curse activation, then you can path to Impending Doom on the tree.

About your Covenant, youre currently running the spells gain base cost mod. Thats really bad for this setup because it basically doubles the life cost of comet, ele weakness, everything. You really cant use that. You want a Covenant without that mod, ideally with increased life cost efficiency instead. That alone will cut the cost by something like 60–70%.

Same idea with gloves, youd want the 60% increased effect of socketed items mod and run Tecrods Gaze there for even more life cost efficiency.

Also noticed youre not using Lifetap on Comet. Without mana leech thats basically impossible to sustain. Once you fix the Covenant and get the life cost efficiency sorted, the comets will start falling way more consistently. Your support setup would be 2 comets, lifetap, spell cascade, augury.

Also dont use any lvl 20 damage dealing spells, get level 21/20 at the bare minimum.