The Shieldbearer is more of an annoyance than a threat. The Shieldbearer's utility is hinged on giving, as you can guess, shields to it's allies. Though it has to move into a prime position because its casts it in an area not on units. All of Shieldbearer's allied units will be gifted with Energy Shield upon cast.
The Energy Shield adds three (3) health shield to all affected units. The Energy Shield adds additional defense, protects the shredding of an armor, however, it can also be used by one Shieldbearer once per battle. For higher levels, the Shield bonus is also higher.
Shieldbearer should be taken out as soon as possible. It is too much work to try and melt all of the Energy Shield from affected units. Killing the Shieldbearer also removes the Energy Shield it provided for the other units. Shieldbearers are organic and are easily manipulated via Insanity and other psychologically taxing skills.
Note: If you are able to mind-control an ADVENT Shieldbearer which already deployed an Energy Shield, the Energy Shield is also gone. So go get him before he uses it to its alien brethren.