This mission is basically a boss fight, but the game removes all of your weapons at the start for some reason. You'll find your jump jet crashed into a fence and you'll be defenseless, but don't worry too much about it, you won't run into any enemies until after you locate some weapons. I recommend you hold onto the shattergun and crossbow (since you will not find a sniper rifle in this level), and the third weapon is up to you.
After rolling through an apartment complex and dealing with some ankle biters (who shouldn't be a problem if you've gone this far on Elite difficulty) you'll come to a ladder leading to a tiny window overlooking Krone's Sentinel. Save here.
Once you jump out, you want to find a corner and put your back to it immediately. There are three quantum timestopping guards with those annoying overpowered surge guns here, who will kill you very, very fast if you stand in the open where they can spawn 360 degrees all around you. They will spawn one at a time, so I recommend using the crossbow, scoping in a bit right as they're spawning, and freezing time to land the headshot and drop them immediately. Make certain you pick up a surge gun at some point after killing all three quantum guards, you need one to finish the boss fight. Once you kill the third quantum guard and collect a surge gun, save.
Now you must engage the sentinel. Choose the nearest plasma cannon atop it (as it usually starts firing at you first anyway) and start unloading primary fire surge gun rounds at it (RT, not LT). Be aware that you absolutely cannot simply hide from the plasma turrets, they will continue to hit you no matter what you hide behind. It will take 10 shots to blow up each plasma cannon, and one surge gun holds 6 when at full ammo. Not to worry, the weapon crates on the floor have infinitely respawning surge guns inside. How convenient.
Once you destroy the plasma turret, save immediately. The Sentinel will rear up and fire a gaggle of mortar rounds each time you blow up a plasma turret, and it will take nothing more than memorization to avoid the salvos and survive this point in the fight. When the sky is clear of mortars, save again. Continue the process of blowing up a plasma turret, saving, avoiding the mortars, and saving again until all three turrets are down.
At this point, the Sentinel will retreat further along the level, and you must follow it through a previously barricaded hole in the wall. You will come out on a fire escape with zero cover and have another weapon crate with a surge gun inside right next to you (how lucky is the protagonist, eh?) and you will want to save here. The final leg of the boss fight is time sensitive, and the Sentinel getting a shot off from the flower gun on the underside will fuck you up immediately.
Use time slow and start unloading surge gun rounds into the blue thing in the center of the flower gun. Hitting the remainder of the assembly will not count as it did for the turrets on top. Once it blows up, the Sentinel falls over. Well done, you just beat TimeShift.
Some pointers for the game in general:
Abuse the saving system! The game does not save a generic checkpoint, it saves your exact progress and location. When you have a breather and aren't inundated with enemies, save!
Time slow is usually more helpful than time stop. Time stop only lasts about half as long as time slow, and the effect of time slow always gives you the ability to dodge most incoming fire.
Never ever attack enemies head on if time isn't frozen. Enough rounds from just one assault rifle will drop you, and enemies are oft intelligent enough to whip a clutch grenade at you if you're charging them like a bull. You're pretty screwed when time slow has eaten 4/5ths of your time power bar and you get a clutch grenade stuck to your face.
I highly, highly recommend you get a shattergun (shotgun) and echo rifle (sniper) as soon as possible and hold onto them for the entire duration of the game. The shattergun is stupid powerful when you get swarmed at close range, and you can often simply camp in an enclosure or corner and blast enemies as they come for you single file. The echo rifle drops everything with one headshot and is very useful against particularly annoying enemies like shielded guards, timeshifting quantum guards, and other enemies with sniper rifles or rocket launchers -- scope in until you get a good zoom, freeze time, pop off as many headshots as you can, hide and recharge time power, repeat. TrueWickedOne adds that a crossbow will kill with one shot anywhere to the body, but beware that it fires in an arc and won't be as effective over extreme distance. Choose your ranged weapon as it fits your style, because it will be getting you out of a lot of difficult situations.
Rocket launchers will always be nearby when you need one, so don't concern yourself with holding onto one all the time.