Toukiden 2

It's dated and a little janky because of that, but one of the few MH style games to really experiment with the genre. The movement abilities, weapons, monster styles, and dismemberment mechanics are great fun, giving it a fast action feel while making the oni still feel like a threat.
I'd buy Toukiden 3 in a heartbeat.

T2 is an excellent action game, similar to monster hunter, but with a better, more involved story and a (mostly) open world to explore.
The world is divided into Ages, and you must get X far within each one to unlock the quick travel to it, in order to complete the quests contained within.
The npcs/teammates who accompany you on your missions, and the story are better than the MH series and play a big part in keeping things interesting rather than just the hunt/carve/upgrade cycle.
The weapons are distinctive, and the skills and abilities used during fights keeps things fun and interesting. The learning curve for each is fairly steep, with plenty of crazy skills and abilities not explained very well (aka very JRPG-like), so keep that in mind.
The graphics are decent, and the music/sound effects are good. Know that the game has English subtitles while all the characters speak (and screech) in Japanese.
If you’re looking for a more Asian-flavored MH with a mostly open world and plenty of monster killing action, I highly recommend it.

This game lets you rip a demon’s arm off and beat it with it. You have a magic ghost hand, anime swords, and a map full of eldritch nightmares just begging for a whoopin’.
Open world? Kinda. Story? Who cares. Combat? Chef’s kiss.
More limbs fly off than in a Mortal Kombat tournament.
KOEI TECMO, I’m begging—Toukiden 3 when??

Definitely not on Monster Hunter’s level, but still a solid alternative. A decent experiment with an open world.

Its a old game, that has some flaws to get it working right, but if you take the time to do so, its a realy fun game! I have it physical on PS4 and PSVita! <3

I had a lot of fun with this game. It's janky and feels dated, but the story is good and the combat is enjoyable. Buy it on sale, not worth the full price, though.

It's really fun and I like it more than MH Wilds in some ways. Companions you can level up and get their unique weapons, characters are more interesting, story is actually decent, weapons are super fun and the mitama system adds a lot of versatility to the experience.