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Bowgun is a tough weapon to start playing Monster Hunter in. But it is the weapon I started with.
First, with heavy bowgun, you have to learn what type of damage mitigation you want to do. Avoiding damage is key in doing well early on. Try to upgrade your weapon to have the shield. This will give you auto-guard. So, if you know you will not be able to dodge a strike, just stop firing, and you will automatically block it. If you are able to find it, try to get Evade, or evade extender. This will make it that much easier to avoid getting hit.
Second: Find any ledge possible. In this version of Monster Hunter, the monsters can't get on the ledges, and can only fire long distance shots onto it. Which means, you can get some very heavy damage done before you have to move from there. There are also areas right before the entrance/exit to a zone that the monsters cannot get into. When the developers made this monster hunter, they were more concerned with you getting your rewards when the monster died, than making it believable and having the monsters just charge through, like in recent versions.
Third, know the weakness of the monsters. Using shots that monsters are weak to, will make the hunts very much easier. If you are going to be hunting mainly from a distance, then learn to use pierce shots, since their power is greatest from 3 hops up to 9 hops. Any closer or farther and it will do less damage.
Overall, remember to have fun, and please, do not be afraid of switching to other weapons, since all monsters have different weaknesses. So while one monster will die very quickly to Heavy Bowgun, another might be a nightmare, or vice-versa.