This story fails so hard in so many ways I can't even begin to describe it.
Character ages. When you're going to screw around with them that much (Tonks would have been about ten to maybe thirteen when she had Teddy going by her canon age) you either have to go back to the beginning of your altered history and build up to the changes, or you need to outline what you've done (which is a technique of either a poor or a lazy writer, but still a better alternative than just throwing changes at your reader and expecting them to accept them).
The Potter's other children: Harry would have been about three when the twin girls were born, why didn't they retrieve him if it was already safe to have children? Why wasn't Harry furious when he found out his parents kept having kids in this 'dangerous' world? People who were abandoned are rarely very forgiving. And kids that grow up on their own learn to sniff out bullshit at much younger ages.
And let's not even get me started on Harry hunting ELDER DRAGONS before he was even twelve. I have played MH, and I call complete and utter bullshit on this one. That, right there, totally broke my suspension of disbelief and saw to it I was completely unable to enjoy this story.
Baby Hypnocatrice. Taming the monsters of Monster Hunter? Not only 'no' but 'Hell NO!'. This is the point at which I stopped reading.
Nicknames. Nicknames are very peculier things and not something anyone can ever choose let alone for themselves. Furthermore, some people simply have the talent to come up with them, and some people totally lack that talent. 'Ri'? Not only is that ridiculous, it's useless, superfluous, and only tells us that Harry's new 'family' is so lazy that they can't even use the two syllables of his name.
Sticking a knife in an electrical outlet would have a higher entertainment value than this story at this point. It's an interesting concept, Harry as a part of the Monster Hunter world, but it needs to be refined so much from this point to make it work. The size and prevalence of the monsters do not fit in 199/X/ Earth. Make sure your story elements don't obstruct each other before you try to do a crossover/fusion like this one. Go back to the drawing board and try again, this story is not worth continuing as it currently is.