Yes, you want as much CDR on all your gear, getting as close to 60% (at least 64% for COE Lightning Archon - but that's a whole different setup for now).
With Gogok and Obsidian you want to be out of Archon as little as possible. 3-5 seconds at most. While out of Archon your only goal is to apply the 3 elements and use Ray of Frost (or some mana (best is the Arcane Torrent, but doesn't work well with Hydras as that as they use the lightning element) spending ability to proc Obsidian) to get back to archon. Once you pop Archon (the 4th element) it'll trigger Tal Rasha's huge damage boost.
Rinse and repeat - since you want to try to be out of Archon for just a few seconds, the Archon stacks via The Swami's ability, and you'll have double the stacks.
IMO - teleporting can be a great defense. If you can move fast enough and know where to dodge attacks, it can help out a lot. So on that note I like to use Aether Walker and Serpent's Sparker.
Equip your better one and cube the other. Main attack is Ray of Frost-Cold Blood (Cold), Teleport-Calamity (Arcane), Hydras-Lightning (Lightning), and Archon-Combustion (Fire).
I put out two Hydras, and teleport around to dodge, while using Ray of Frost to speed up the cooldowns. Once archon is ready to go, you can deploy two more hydras to refresh their timers (how long they can be up) before popping archon.
There are alt builds that replace Teleport with Black hole, which can give you great amount of damage multipliers ontop of manald heal and tal rasha. But with a build this squishy I prefer Teleporting around.
Also to remember - make sure your highest elemental damage is Lightning (usually the bracers have this skill - don't waste it on re-rolling on the amulet). As that is what element will be used when in Archon form.