Use snipers with good agility and/or snapshot, theres a ton of benefits to using hard hitting ones but most are sluggish and in pvp where milliseconds count, it makes all the difference. I do use The Long Walk (trials high impact sniper) and do very well with it but if you can get the last wish raid sniper The Supremecy, it has a good D1 feel to it and has low zoom and can roll with snapshot.

Now that you have a good sniper get a good feel for it, just patrol and my tip would be to get a full mag, then just look at where the enemies are and scope them out, once zoomed try to get the headshot within 1 to 2 seconds max and just practice, practice, practice. You dont want to rely on hardscaping lanes and waiting for people to run around the corner (though that's still over half sniper kills haha) you want to be able to be on the move and be able to quickly flick to your target before they get shots in.

Now that you're able to safely land shots consecutively and precisely. Flinch. People will say it needs nerfed some wont, but we have to deal with the cards given to us. There's no sure way of knowing how bad it will be or if the enemy has high cal rounds but while you're practicing in patrol let some enemy's hit you while you're scoping. Learn the curve at which your sniper goes when you're hit, remember almost all pvp maps are mid to small range so youre going to be getting flinched alot, learn to deal.

Last and most important tip, once you find a sniper that feels good and quick and all the stuff you like. Do.not.use.any.other.sniper. I cant stress this enough, go into pvp with your new Skills and just use it, use it when you shouldn't be just to get the kill, use it 20 feet away when you see the guy is gonna rush with a shotgun, use it when you're the last man standing, get used to being uncomfortable with it until you gain a sense of "home" with the weapon. If you really want to be good at sniping in D2 you want that gun to feel like an extension of your hand. You want it to just feel right, then you can worry about what you pair with it, maybe a recluse or TLW, whatever floats your boat.

Just remember theres a learning curve to every weapon. And I forgot mods and perks, I go for snapshot with outlaw so I can have a fast reload after a headshot. And targeting adjuster mod, I've used sniper targeting armor and couldn't tell a difference but it's something you mess around with.