The lights are on
You'll need a weapon like the Cain, along with squadmates who are well-outfitted with their respective upgrades. My choice of weapon for Shepard is the Widow Sniper Rifle, easily the most effective and most powerful weapon players can use short of a heavy weapon. The Viper Rifle is less powerful, but useful if it is fully upgraded as well. For other classes, if you have not downloaded the Mattock, Geth plasma shotgun, or the Locust (Kasumi's Stolen Memory) then do so, as these are great alternative weapons to use for other classes.
As always, the terminator-esque Human Reaper usually begins by firing a large burst of energy from its chest, so you'll want to find some cover, preferably in front of you. Note that after a while, the Human Reaper will change its position, but if you keep your distance and maintain cover, you should be safe. Getting hit by the Reaper's chest beam instantly depletes your shield and causes a delay in recovery, so be cautious. Note that it also increases the wait for your shield regeneration substantially.
Equip your weapon of choice. While keeping yourself shielded, just aim at either the Human Reaper's eyes while it's charging up its attack. For a long-range shotgun like the Geth plasma cannon, charge it up and shoot at the chest. Eventually, you'll get's health down to three-fourths after a couple turns, depending on your weapon and character upgrades.
With this damage, if timed correctly, the Reaper will usually unveil its tail attack and accidentally destroy whatever platform Harbinger is on.
With your Cain heavy weapon, wait until you get to just under half of the Reaper's health, then use it, aiming for its chest or eyes. The astonishingly powerful weapon should end your battle in no time. Presto! You've beaten the game. Now sit back and enjoy the wild ride.
Most useful powers: Field Throw, Unstable Warp, Incinerate, Concussion Blast, Tactical Cloak, Warp Ammo, Shredder Ammo