I'm a little past ego level 900 now and did most of it with a bolt action sniper rifle. Only tips I can give really are:
- Aim at the chin/neck area, the head hitboxes are goofy.
- There's no bullet travel time, so aim where they are, and just lead the target a little if they're moving.
- Find and use anything that will crank up your crit damage, that's your bread and butter.
- If you snipe from far out (maybe 100-150 yards?) and one-shot enemies, it won't alert the rest. You can take out entire camps without anyone seeing you sometimes. If you miss though, they'll spot you, so take careful shots.
- Learn the crit hotspots on all the enemies (it's not always the head, there's enemy videos you can earn via pursuits that tell you what they are, otherwise trial and error)
- If you're being fired at by riflemen enemies, make sure you have cover nearby, they're pretty accurate even at long ranges so don't depend on them missing.
- Set up your secondary weapon for close/mid range for when the enemy manages to close the gap. I used an Assault Rifle since it has the most versatility.
- Watch and learn the patterns of enemies, many of them will have moves that telegraph moments where they're going to stay still for a bit (and thus a good opportunity to get in a headshot). Additionally, learn to pick targets by which ones are the biggest threat to you.
- Try to get higher ground when you can (and get the perk as well), it gives you more area to survey, and it tends to confuse the AI in terms of getting into melee range.
Other lads have given you great tips but one of the best ones is to breath slowly and keep calm else you'll be missing more than you should.
To get moving targets, just aim ahead and let them run into the crosshairs.
If you're on PC, I'd suggest turning off aim assist.