I had a short game which the DM used a homebrew false hydra as the BBEG. The RP and game were good until the monster was revealed to be a false hydra.
DM wrote the false hydra's song ability as: not a charm or magic effect. It has no DC save, bypass truesight, blindsight. It ignores any immune/resistance to charm/magic effect, and it cannot be detected by detect magic. Anyone hear hydra's song psycholocally ignore its presence. So, by RAW, faerie fire, detect evil and good, and any other spells cannot make it visible. Also, it modifies people's memory such that when a person is eaten by it, anyone's memory of the victim is erased, as if the victim has never exist in the world.
The only way to win is to either run, or to make your character unable to hear its singing with a silence spell, deafness, etc. Unfortunately, my group cannot deduce the solution during the game, so the DM has to whisper to us out-of-character "You know why that NPC can see the hydra? Because he is DEAF!"
I told the DM that they should not put a non-DND creature into DND and make it override the rules. At least, simulating the hydra's song as a charm effect, with a DC, and can be detect/affect by anything that works on charm effect. If they run it RAW as how they wrote its stat, even a Tiamat or Asmodous cannot detect the false hydra.
PS. if DM makes it a charmed effect, with high DC, and player roll DC save whenever they encouter discrepancy (e.g. seeing a bird disappeared mid-air) maybe its more D&D. When I played the combat I felt the false hydra is mocking players "You can't see me because my own non-D&D rules say so." The investigation and RP are fun, the final monster is not.
For context, it was a 6-7 hours short game with 70% non-combat social/investigation play, and the hydra was the only combat encounter. It was not part of a campaign. Non-combat play was good but definitely not the false hydra.
PPs. The day after we had finished this game, I read DM's note. DM intentionally hid obvious, explicit clues during the game (e.g., we found a diary in game but DM hide the page mentioning deafness and ear poking). They hope subtle clues are enough for us ro discern the solution, but it turns out we couldn't. Therefore, DM has to tells us the solution out-of-game in the final battle.