What is this "thing", exactly? Being non-linear? There's many linear metroidvanias out there, in fact most Metroid games are. The qualities the Metroid series is known for are there for sure.

#28: Makes me think of Perfect Dark. Is it that one?

#33 - The bad guys use a flying pirate ship to freeze stuff.
Hint 2 - They wear all-black outfits in this sequel, whereas they wore all-white in the previous game.
Hint 3 - There's an optional tournament mode where you can fight against the "bosses" from earlier games in the series.
Hint 4 - Though it's from a long-running series, this is the only mainline game to have a number in its title.

So yesterday was a good day for guesses. #31 was guessed after some tries by coolbeans; Motocross Madness and #29 was guessed as well by GoOnKid who correctly guessed SoulCalibur. Here's a second hint for #30 and we continue to #28.

#30: The battle between these two belligerents continues this time also over sea and air.

Hint 2: You shouldn't click on the boat and stop rocking it, because you're making him seasick.

#29: First there was an evil sword that changes appearance depending on its wielder, but in this game, there's a spirit sword made to combat it. Guessed by GoOnKid - SoulCalibur

#28: Originally this game far supposed to feature a male protagonist, by the designers figured that then it would look a little too much like James Bond, so the decided to have a female star instead.

So yesterday was a good day for guesses. #31 was guessed after some tries by coolbeans; Motocross Madness and #29 was guessed as well by GoOnKid who correctly guessed SoulCalibur. Here's a second hint for #30 and we continue to #28.

#30: The battle between these two belligerents continues this time also over sea and air.

Hint 2: You shouldn't click on the boat and stop rocking it, because you're making him seasick.

#29: First there was an evil sword that changes appearance depending on its wielder, but in this game, there's a spirit sword made to combat it. Guessed by GoOnKid - SoulCalibur

#28: Originally this game far supposed to feature a male protagonist, by the designers figured that then it would look a little too much like James Bond, so the decided to have a female star instead.

After the last games were all guessed early, these ones seem to be a bit more difficult. More hints:

#31: Transferring the soul of an animal into a child born without one will not end well. Anyone surprised? Killing a god may the cause of it all. You are the Watcher.

#30: A-Plus, Akebi, Ramen, S-Chan and just Frank. Deliver the cleaned laundry. Actually you forget to deliver it.

#29: The rooster of war! The tree of love! This colorful open world game let you interact with some gods.

#28: Climbing, swimming, running, flying, digging... and freezing. Luckily there are hot springs, which will warm you up.

More hints on my games:

34. a) This first game in the series was based on a classical piece of literature but not European literature.
b) The literature is about outlaws from a marsh, but the video game also included elves and dwarves and other fantasy tropes that they thought would appeal to a Western audience.

33.  I bought a SNES on launch day in order to get this game.  Given, the game didn't release until sometime the next year, but Nintendo Power said it was coming, so I just had to have a SNES as soon as possible.

32.  This game is probably the main reason why the Wii holds the NPD record for most hardware sold in a single month.

#33: A Link to the Past?

#32: New Super Mario Bros. Wii