But what if I wanna play the whole thing solo?
I didn't know this had time limits. Keeping expectations in check since I utterly hate time limits.
The time limit is very, very generous, I've only ever been up against it when tackling online- only beasts (meant for 2-3 players) solo, whereas we don't know how they are balancing the hp pools of the beasts here yet. Even then, if you are outmatched to the point where you can't kill or capture it in 50 minutes, it's far more likely that it'll KO you three times first unless you run out the clock by fleeing to camp every ten minutes.
Usually it takes you two minutes at most to find the monster, and even less if you've got skills or equipment that mark it for you. If you can't take a monster down in 50 minutes solo, you're usually severely under-equipped. MH doesn't have levels, your power level is only the gear you have, so if you aren't doing enough damage, you need to upgrade or tailor your weapon, tailor your kit bag with appropriate items and check out the skills and offensive/defensive abilities available by skinning the beasties one step below the mark you're struggling with, then come back.
Honestly, it's really only an issue if you are woefully outmatched or under-prepared, in which case part of the fun is learning it's patterns, going away and thinking about a setup that will take it apart. That feeling when you take down something that forced you to back off before is awesome.