Buzzkill is actually a pretty cool mission, but you need to have a rigth set up for it, and for most of these with lots of targets to shoot.
Refit your ship at minimum or just go with a different one entirely. If you stay with a battleship, then go with double prop, MJD + MWD and sniping. You need to be doing at least 600ish DPS at 100+ km, 900 to be comfortable, and anything over 1050 will go super fast. Armor ships in particular are super easy to fit for this because their tank goes into lows. If you use a shield ship, you end up dipping into the tank.
Carry at least 2, if not more ammo types with you. 1 for long range, 1 for precision and 1 for highest DPS.
Not all laser crystals are good for same things, you will notice some of them have tracking penalties, those are bad to use against frigates at close range, some have range bonusses, etc. Check which is which.
When you MJD out of range you have a timewindow to snipe all those frigs as they try to close in, anything that gets below 50 or around tehre you should just kill with drones. If you get too many that get below 50 you can switch to precision ammo in addition to teh drones. Once your MJD is of off cooldown, recall drones and jump away again, rinse repeat.
Its a PITA, and also not everything always goes according to plan. Sometimes you wanna go into orbit on something, or move a bit closer or further to maintain a ceirtain range, or have to loot a mission objective. Even when you triangulate to perfection you still have that cooldown between MJD jumps, + you can swing out on warps. Its up to player preference, but the flexibility of MJD + MWD is just awesome and too hard to give up.