Long Night of Solace is a long mission, so I recommend running it on Easy or Normal to speed things up. At the beginning of the mission, just run by any enemy that's not directly in your way on the beach, and prioritize the Elite Ultra that lands just beyond the dropship on the way into the Saber Facility. Kill him first, then mop up everyone else to get into the facility. Kill the Elite in here with a noob combo, and on the way to the saber grab the stray Energy Sword.
In the Saber space combat sequence, you have waves of enemies to deal with, then a gunboat wave. Make sure if you're on lower difficulties you follow the tutorial prompts immediately to save time. Prioritize trying to get multi kills on the arriving Banshees in the first waves to quickly dispatch the easy targets, then follow the game's advice and strip shields from Seraphs with your guns before switching to missiles. Three or four rounds of missiles on the gunboats will destroy them, so when they spawn in immediately target them; the rest of the enemies will bug out once they're destroyed, but if you kill any stragglers that will speed things up. Immediately head to the hanger so you're there to start the next cutscene when the waypoint gets dropped.
The next section is the space assault on the Corvette. At the beginning, head under the ship, and aim at all the docked ships for a nice multi kill, then prioritize the engines. Once the engines are toast you'll need to kill a few more Seraphs, then land on the ship.
Once on the ground, grab your sword and immediately drop down into the center of the bridge. There are four Elites you can quickly dice to open the door out of here, and you should have enough energy to waste everyone in this hallway. In the shuttle bay, kill the Engineer hovering up high in the center of the room to remove the shields off everyone else, and then headshot and noob combo everyone to death. If you position yourself up on the gantry where the button to open the bay for the Pelican is, you can save a few seconds.
Once the reinforcements have arrived, if you want you can just charge through the new enemies and leave them for your allies to contest. You're going to want a plasma pistol + headshot weapon for the assault on the bridge. I recommend just beelining straight for the Stealth Elite in the center of the room, assassinating him, and then targeting any other stealth elites before they can cloak and be a nuisance, then the Elite with the power weapon. Once the room is clear, hit the switch towards the back of the room from where you came to proceed, and then head to the exit; chucking a few grenades at the entrance can wipe out the assault team they send in after you.
From there, proceed to the shuttle bay, and kill off the waves of enemies; the initial ones will come from the side passages, followed by Grunts out of the elevated door to one side, followed by Elites from another door up a bit from the last one. Headshots and noob combos will make everyone go down easily. There will be a last group of heavily-armed Ultras to take out, and then make your way to the back of the Pelican to end the mission.
On my first run on Normal, dying a few times on the bridge, I still made it in 18:30, so you have plenty of room for some errors and goofs.