Biggest peice of advice as far as actually gunning goes is always be in crit range. The actual distances can be found with resources online that I don't want to search up on mobile (sorry) but you'll know by a visible screen shake if you're in it. It raises attack sage by 1.5 which is huuuuge. Looots of gunners ignore this, and that's one of the major reasons people do poorly with gunner weapons.

Additionally, gunner weapons appreciate research much more than blade masters. Because y ou have a limited (albeit very high) number of useful shots, it's in your best interest to make each of them count by ensuring you're always hitting a monsters weakspots, whether it's to shot type or elemental damage.

As for sets I always advocate mixed > anything so just a run down of skills that are really useful to heavy bowgun:

Evade distance +: some consider it staple others a waste. Personally I count among the former. Evade distance gives you so much mobility which is the major down side to the weapon. It helps alleviate the problem of having to quickly reposition into crit range by making your main source of movement go further per use.

Attack up: flat damage is hot. With limiter off, you get more out of it because hbg does damage based off listed raw for the physical shot types, and removing the limiter raisers your weapon multiplier from 1.5ish to 1.7.

Crit eye: there is a certain attack power where crit eye starts out damaging attack up. Frankly I don't know it off hand but if you really want me to I can calculate it when it's not 3 am.

Weakness exploit: raises damage and affinity when hitting weakspots. Relatively big boost for only 10 points

Challenger 2: king of damage skills. Monaters rage a lot. Free stackable attack up and crit eye boost.

Shot type up: most heavy bowguns focus on 11 of 2 main shot typws: normal or pierce. Having the respective shot type up skill gives you the most damage point for point than any other skill. Basically mandatory.

basically you get evade distance up if you feel like you need it and then just stack damage skills.