Teodor cannot be cured. (This is not true at all, while he cannot be cured by players, he can be cured by NPCs, trusts that use AoE heals are highly recommended, Selh'teus's Redemption heals for extremely high HP and Apururu's AoE Cures work too)
Tank recommended to mitigate Area of Effect/conal moves from Hades.
MP replenishing items for mages recommended (vile AND vile elixir +1). At least one of your healers needs Stona. Second form has a dispelling move.
If you used any your meds on first fight, take the time to go back to town to buy more.
If you fail, you must zone out and zone back in to receive a new key item.
Hades shifts between different elements. His attacks differ depending on which element he currently is.
Paying attention to Teodor's nukes will tell you what element he is currently. For example, if Teodor is casting Fire V on Hades, then Hades' current element is ice and he will use his ice elemental attack that causes Paralysis.
Occasionally he will be blue proc'd. It's assumed that is when he changes elements. Certain TP moves that Hades always has access to may also do so. Or he may switch after a certain amount of time has passed.