Hint 1: Why does the earth rumble?
Hint 2: I make a hat out of my defeated enemies!
Hint 3: The city at the edge of the desert is replaced by a port town in the remake.
Hint 4: Something Devilish can turn up unexpectedly in other battles.
Hint 5: Cha-Cha or Kayamba?
Hint 7: The franchise for this games makes people on the internet angry each time it switches the platform. With this game it switched with the original AND the remake to Nintendo.
Hint 8: Really? No one got it yet? Well in this series you go on a hunt and meet Monsters.
Monster Hunter 3?
As guessed by Flilix, it is Monster Hunter Tri or 3 Ultimate (also 3G in Japan).
I was triple-dipping for the game, on Wii, on 3DS and WiiU. But 3DS in my opinion wasn't a good platform for this game, so I only count Wii and WiiU versions for this list. The remake on WiiU had some graphical improvements, most notably obviously the resolution upgrade to HD. Also it contained a lot more content. Still, I consider the base game relevant here, the basic gameplay is what makes this game so addictive. So I count both versions together.
The basic gameplay is killing monsters. The fun in it is, that this is no easy task (at least for the big monsters). It may take half an hour to bring down a new monster you haven't met before. You must learn it's moves, learn to dodge and wear the monster out until you can place some hits of your own. Also good preparation is important, each monster has unique strengths and weaknesses, choosing the correct equipment can make a difference.
I am not alone, especially in Japan this game series is very successful. As it is an exclusive mostly, this spawns regularly heated discussions if it switches the platform.
This game also incites artists. Look at my avatar for reference, or this:
Overall a great fun package, you shouldn't miss out.