The par score for Regret is 25,000 points. Following my method, you will be playing on heroic with some skulls and taking your time. The par time for this level is 15 minutes, which is hard to meet even if you rush.
Since we won't be worried about time, you can put your scoring and HUD settings to just 'score'.
Catch - Enemies throw more grenades.
Famine - Weapons dropped by AI have half ammo.
Fog - No motion tracker.
Iron - Dying restarts the level. If you die, save and quit immediately, then resume the level to keep you points intact. This will reset your killstreak, however, so you won't be earning as many points per kill as you were before you died.
Jacked - You cannot board ground vehicles except by hijacking. There are no vehicles on this level to drive.
Use the beam rifle you get at the beginning to take out elites and jackal snipers.
There's a couple hidden carbines in the circular room with grunts and jackals not too far into the level. If you hop over some blocks, there a little outside part you can crouch and drop into with carbines.
When the phantom drops some hunters, use a combination of grenades and beam rifle to kill them. I found that the grenades would sometimes turn them around and I could get an easy shot onto their back.
For the rest of the level keep a combination of either carbine+beam rifle/sniper rifle or carbine+plasma pistol. Sniper rifles are great at taking out elites even in close quarters because it makes them flinch and allows you to line up another shot.
The big room with the holographic regret is the most difficult portion. Take out everything you can see before moving forward because more enemies will spawn as you proceed. Back up if you have to because the drones and snipers can overwhelm you. Try and grab a beam rifle to take out the hunters and honor guards. Once everything's dead, grab a 'fresh' beam rifle for elites later on.
Note: When I was playing, the honor guards disappeared. I spotted them, but they weren't rushing me with their swords, so I focused on other enemies. I looked everywhere in that room for them afterwards. Totally gone. They're worth a lot of points, but there are plenty of honor guards later.
After the hologram room, the final room of that structure that has the underwater transport you need to activate has an invisible elite with a sword. RIP the marine that somehow survived until this point only to die by that.
Before activating the final gondola, grab a human sniper rifle from one of the pods and stock up on ammo. It can easily take out the honor guards in Regret's chamber.
You can use the rocket launcher on the gondola to take out the phantom's turrets. They're worth more points than the banshee's that show up. Yo should have one shot left to take out one of the banshees. Avoid the shots of the second one, it should leave you alone eventually.
I landed on the final structure with about 22,000 base points. I was worried I wasn't going to make it, but the honor guards in the final room are worth over 1000 points each. Don't skip out on them!
You'll need to board Regret 3 times to end the level. As the fight carries on, more enemies will spawn, including honor guards. I stuck to the corridor in the back to the right of the entrance and boarded Regret when he got close to me.
I died a lot on my first try but was still able to get ~31,700 in 35 minutes. No time multiplier. The more you die, the less points you'll make because you restart your killstreak every time you save and quit. If you play more carefully than I did, you should be able to top my score.