Taen is an enemy found in the Tenebrous Reef. It is considered the hardest boss except for Tenjin and Final Tenjin and should not be attempted until most other sidequests are completed.
"The impenetrable exterior yields only to repeated elements."
This means Taen can only be damaged by the element of which he was last hit. If you attack him with lightning then he'll get a "Last Hit" state with a lightning bolt added next to his name. That means you can now only damage him with lightning. He will frequently hit himself with different elements forcing you to adjust. The elements he uses on himself are lightning, water, wind, earth, light, and dark.
He has two HP thresholds. At 70% health he uses Epoch Shadow which drains half of the entire party's HP and 100 MP. Around this threshold be prepared with MP healing items.
At 35% he uses Infinity Blade which is 20 physical sword attacks in a row. If possible, try to have everyone who is not attacking use Charge before crossing the threshold to reduce damage significantly. Otherwise be prepared with Enda's Healing Wind 3 and Ex-Heartens.
If you don't want to take the effort to match whatever "Last Hit" state Taen put on himself, you can use the Replay spell (via Xero or his shard) to ensure that a character gets to move twice on their next turn. Have them use an inexpensive skill of their main element (preferably a "Wane" spell), and then follow up with a strong skill of that same element.
Turn x8 - Healing Drop 3
Above 30% HP - 4 physical attacks
Below 30% HP - 5 physical attacks
70% Threshold: Epoch Shadow - 50% HP drain and 100 MP damage.
35% Threshold: Infinity Blade - 20 physical attacks (x0.5).
Focus - Self heal 2000, remove stat-ups and downs, buff ATKx2
Speed-Cut - Physical attack (x1.2), boost own AGI, changes Last Hit to Light
Fire Swipe - Physical Fire AOE (x1.0)
Flux - Lightning magic damage (x1.0) on entire field.
Shadow Flux - Dark magic damage (x1.0 + 400) on entire field. Blind 80%.
Earthquake - Earth magic damage (x1.0 + 800) on entire field. Lowers MDEF.