PS player, where are some of these enemies?

[kev]

There are trophies for finding some ... obscure ... enemies.
1) Tengu in the forest
2) Maneki-Neko in the cauldron

So, are these just really rare enemies that show up in random and/or fixed fights? I've noticed that barely 1% of players have found either of these.

[TheMetal]

They aren't random encounters, and instead hidden bossfights. The tengu in the forest you can only fight if you refuse to give him the 3 feathers in the forest dungeon, if you've already given them to him I believe you're ♥♥♥♥♥♥ until next NG cycle. The Maneki-Neko is a secret boss in the cauldron dungeon, you have to offer a "large gold" (according to google translating the JP wiki) to the cat statue on cauldron layer 2. Can't be more specific with the second one because I lost my entire endgame party before I could reach it and I'm waiting a bit before starting again, sorry.

[Helix Uranus]

The Meneki-Neko needs an Oban, dropped initially as Old Money(?). I found mine on the same level after hours and hours of farming.

[kev]

Oh, nice. Oban can be found more commonly in the volcano area. Cauldron layer 2 for this Neko? I'll start punching walls.

I also figured that I couldn't fight the Tengu because I handed over all the feathers. I guessed right but that doesn't make it any less obnoxious.