Could you show me which setups you used? I'm curious to see a player's build.
The Phoenix was intended as a late challenge and is meant to be strong, but beatable on month 10 or 11. Ideally you should have the demon twins or the angel/devil babies, as thy provide strong attack stats and have useful skills.
The poltergeist drops an ice sword that affects normal attacks. You can use the sword with the tentacle/demon twins double attack chance to exploit the weakness. The poltergeist has a counter/reflect skill that can buy you a turn, but it won't damage the phoenix if it uses a fire spell (which it does more than planned...hmm.)
Other viable strategies should be using the pixies' water spell, summoning pixies/fairies by having Titania or Oberon, growing an offensive babies for 5 months for stronger damage (elf and fox last 12 months), or trying to repeatedly disable the Phoenix with the Demon Twins/Twisted Twins skills.
ALL THAT SAID, balancing is hard and I didn't have enough time for the Phoenix, so there is a chance it cannot be beaten. I may revise its stats and AI, as it's spamming Fire III more than it should and going faster.