In order for a Barrier to count as "Warped" the Barrier must dispelled(As in the last part of the bar must be depleted by it) with a Warp attack, Warp Ammo does not count.
Barriers are the rarest form of protection on enemies, mostly found on Collector Troops and Harbinger when he assumes control of one.
If you instruct a Squadmate who has Warp to warp the barrier manually via the power wheel or D-pad shortcut it will count for the trophy, if a Squadmate dispels a Barrier with Warp on their own accord it will not count.
Warp is Available to Adept and Sentinel Shepards.
Squadmates with Warp are Miranda and Thane, and Liara in "Lair of the Shadow Broker"