To beat the Phoenix bosses, it's best to have the following: Characters around level 120 or higher, the best high level armor and weapons for every char, 20-30 SP Potions, 20-30 Super Potions, and at least 10 Elixirs. You can farm elixirs in the same area from the boss-like monsters.
In terms of skills, Explosive Strike on Eefat, Full revive on both female chars, Dragonrun for Viper, Heal All (at least 500 hp) on Clia, and the most important skill: S(trength) Up All on Clia!
With S Up on all your chars, even Harty can do 3000 damage crits with Triple Shot! Both Eefat and Viper will crit in the 2000s. Without S Up All, don't even bother attacking. Harty will do something like 100 damage, and both Eefat and Viper will be doing ~500 per attack. If S Up All is not on, use your attackers to pop potions so that Clia can use her turn for S Up All! I found the Poison Blade skill to be near worthless, as it only did 100 damage per turn. In the end, it maybe saved me 3-4 attacks, so that one is up to you. It's also annoying to have to wait for the 100 damage pop-up at the beginning of every Phoenix's turn.
You will need to get lucky because if all four Phoenix cast their elemental spells a couple of times in a row, you'll lose at least Eefat and Viper. If anyone gets physically attacked twice in one turn, they will die. Save your elixirs for when Clia is dead and low on SP or if both Clia and Harty are dead. Otherwise, just use Clia/Harty's revive skills, or use Eefat or Viper to throw some potions for additional healing in emergencies.
I would focus on the Red Phoenix at the back, since he casts S Up on himself, and will drop anyone in one hit with S Up. Then I'd move to the Blue, and save the Green for last, since he casts D Up and takes the longest to kill. Each Phoenix has 20000 hp, so it's all about a few lucky crits. Once you've dropped the first two, you've pretty much got it in the bag. It's not too hard. Good luck!