Pull - Grabs the shield out of an enemy's hands, leaving them exposed.
Stasis Bubble - Stasis Bubble (level 6 stasis upgrade) will cause an enemy to drop their shield. Sometimes they seem to block the initial hit, but as soon as they move at all, they get caught in the bubble trap and the shield falls.
Armor Piercing Ammo / Piercing Mods / Widow, Black Widow, and Javelin Sniper Rifles - Ammo, mods, and weapons that provide an armor-piercing capability allow you to fire THROUGH a riot shield (and other light cover). The M-98 Widow, Black Widow, and Javelin sniper rifles have armor-piercing rounds by default (no ammo or mods necessary). In multiplayer, armor-piercing rounds can be purchased at the store and equipped on the "Equipment" screen.
Well-Aimed Headshots - The Cerberus Guardian's riot shield has a view slit right at head level, and you can shoot through the slit and score headshots if you've got good aim and an accurate weapon. The "Mail Slot" achievement/trophy is awarded for killing 10 guardians in this fashion.
Singularity - If you aim above or to the side of an enemy holding a shield, sometimes you can get a singularity to "curve" and hit the enemy from the side or behind, avoiding their shield. The enemy will drop their shield if they are caught in the singularity. It's a little tricky, and doesn't work in all situations, but with some practice it can be effective.
Forceful Attacks - Many special powers will cause an enemy with a shield to stumble and lower the shield temporarily, giving you a window of opportunity to shoot them while their shield isn't blocking them. Includes, but is not limited to: Throw, Shockwave, Charge, Nova, Concussive Shot, etc...
Flank / Combat Drone - If you and a teammate can flank a enemy with a shield, one of you should have a clear shot - The shield only faces one direction. In the absence of a teammate, a Combat Drone can be deployed behind or to the side of the enemy to attract their attention.
Yes! Aim for the head (or head-analogues)!
One of the loading screen tips alludes to this directly, but there are half a dozen other clues that you get bonus damage depending on where you shoot - the equipment which "increases headshot damage by X%", for one, and the multiplayer kill achievement for another.
Perhaps most viscerally, scoring a solid headshot on a humanoid opponent will cause their helmet to explode in a brief fountain of gore.
So aim for the head!
Best Answer
Even if you are cloaked you're not completely invisible. As far as the cloak goes you'll see a little field of electricity every now and then. Also, certain enemies are smarter than others; assault troopers won't see you unless you fire but let's say a banshee or a phantom were there, they would most likely be able to see the background morph as you move.