Shroud Reaper is easily one of the most annoying sections in the entire Mass Effect trilogy that is contained in Legendary Edition. Here is how to beat or even speed run through it.
Shepard doesn't fight the Shroud Reaper on Tuchanka directly and will be spending time dodging its legs as well as the Brutes it drops on the squad instead. Depending on the version of the game you have, you can go through this encounter by running past the Brutes, killing them or combining the two strategies.
Running for the Hammers
The quickest way to beat the Shroud Reaper is to completely ignore the Brutes and just run for the Hammers. Infiltrators can have a slightly better time than the rest since the Tactical Cloak can confuse Brutes, making the dodging slightly easier. Keep in mind they will still detect you at close range.
As long as you're sprinting, you should be able to make the distance between you and the Brutes so just head straight for one of the Hammers. If you're not sure about their location, press the map key to show you the objective locations.
As you approach either side's hammer, you will start seeing a giant shadow on the floor - immediately dodge to the side or backwards to avoid getting instantly killed. Brutes will catch up to you at this point but you can use the nearby Krogan monument to block the line of sight and prevent them from charging. By the time they waddle their way to your location, the Reaper's leg should lift and you can just sprint towards the Hammer to activate it.
At this point, you will need to sprint back through a group of Brutes so it would be great to chuck a grenade at them to stagger the group or make them assume a defensive position so you can move past them. After you go through the Brutes, you're safe to sprint all the way up to the bottleneck before the second Hammer, at which point you will need to repeat the shadow dodging manoeuvre from before. When the Reaper lifts the leg, ring the second hammer and watch the epic cutscene.
Fighting the Brutes
Regular Mass Effect 3 will keep throwing Brutes at you indefinitely. Therefore, you should only fight one or two at most at any given time, in order to clear a path to run past them and ring a Hammer. Meanwhile, Mass Effect Legendary Edition will let you get rid of Brutes for good so you can just mow your way through the battlefield.
To maximise your chances, make sure you bring a lot of armour-busting gear and abilities. This includes slow but hard-hitting snipers and shotguns, incendiary ammo, grenades, powers like Incinerate or anything else that was upgraded to be effective against armour.
Infiltrators have the easiest time with fighting Brutes thanks to access to sniper rifles, Tactical Cloak and Sticky Grenades. You can stealth up, throw a Sticky at a Brute and then headshot it with the rifle. Stickies don't break stealth so you will still get the bonus damage, allowing you to down a Brute in just one shot. Widow, Viper and Kishock Harpoon Gun are the best weapons for this strategy.
Just like in the running strategy, you will need to be on the lookout for Reaper smashes - as soon as you see a shadow starting to appear nearby, dodge back or to the side. Do this on both sides of the battlefield and you will be treated to a kaiju vs kaiju cutscene.
While this strategy is slower than just running, it's a bit safer since you get a few moments to figure out what's what in the shaky mess that is this encounter.