"This hulking, four-legged monstrosity prowls the landscape ceaselessly. Its protuberant head scans the horizon slowly in its ageless quest for timelost prey."
This enemy can easily endlessly stun and then kill you, especially if you have low DV. As a robot it can be disabled with an EMP grenade, but only for a few turns.
Since explosions ignore AV, it's best to approach them with high DV gear to flinch out of the way of their projectiles more often.
Try to avoid standing near walls when engaging them as, even if you flinch out of the way of their projectiles, the projectiles can still damage and stun you if they hit a wall near you and explode.
The most effective way to take a Leering Stalker down is to disarm it and then maul it with a Vibro Blade or Ceremonial Vibrokhopesh. The simplest way to accomplish this is with the Swipe and Dueling Stance skills from the Long Blade skill tree. After activating Dueling Stance, get within melee range (preferably after stunning it with an EMP grenade) and then use Swipe. Assuming it failed the strength save, it should drop its blast cannon on the ground, rendering it substantially less dangerous. Do note however that it has a melee attack that it will resort to if disarmed, though it is rather weak and shouldn't pose too much of a threat to characters with high AV or DV.
The blast cannon weighs 70 lbs. and yields AI Microcontrollers as its highest-value bits.
Leering Stalkers drop Antimatter Cells more often than seems random.