Unspent credits will carry over into the next sector, so don't worry about spending all of them.
New equipment slots and a few of the ship-specific perks are also very useful.
When unlocking new perks, definitely focus on energy and speed perks.
No Subroutines or Glyphs can be selected.
No Ancient Structures will generate in the run (excluding the one in Sector 7).
Be comfortable with hard difficulty before attempting this mode. Hardcore is an extreme challenge, as it limits Perks and introduces a new handicap mechanic.
Scrap is the most common resource and is yielded from all equipment when salvaging.
In the early game, save your access keys for getting Subroutines from derelict Colonial stations.
The energy and speed perks are also very important.
A good pilot perk to focus on leveling up first is Credit Loot Bonus, which will let you progress much faster.
Don't be afraid to stop while exploring - use freelook to look at your surroundings and plan where to go next while your energy core recharges.
Energy recharge doubles when not moving or firing (after a short delay).
Check out the G&B, Okkar, and Outlaw pages for enemy ship info.
Try to get behind enemy fighters - they can't shoot at you, but you can shoot at them.
Be careful when boosting in combat - it helps with dodging damage, but firing and boosting at the same time quickly depletes your energy.
It also saves energy, as boosting is not needed. Alternate strafing left/right and hovering up/down - this will make it very hard for enemies to hit you.
Once you get a feel for the movement, try to master circular forward or backward dodging.
After completing the story, Colonial warships will stop jumping in, and there will only be three waves of Okkar ships.
The Okkar that jump in after taking too long in a zone can drop fuel and occasionally credits, but otherwise they won't drop anything.
Crafting consumables and secondaries and using them while pausing is very useful in fights.
Stay calm - panicking will often get you killed.
Mines will often spawn in scrap fields and near derelicts - if you're in a tight location, scout around with the action freeze to look for any nearby mines you might trigger.
Prioritize comm hubs if there is one in a zone - they will often reveal containers or other loot you may not have seen without them, as well as letting you prioritize more rewarding parts of a zone.
You don't have to kill every single enemy, but you miss out on possible rewards.
Don't be afraid to use consumables and secondary weapons in fights - faster battles usually means less damage taken.
If playing in Hard or Hardcore, make sure to manage your time well, so you don't get interrupted by the Okkar.