The Bat is a basic offensive melee monster and is very annoying when encountered in Frostburn, in the campaign.
Bats are highly aggressive and when they reach you they drain your troops' blood, dealing constant, albeit very low, damage (4 or 5 hitpoints). They have low health so it's best to attack them with ranged troops.
They are offensive monsters and so use a speed boost. They have fast movement speed, very low HP, low attack power but extreme attack speed, and an annoying special.
The Bat's special is to dash through the enemies. His special is similar to the Wolf's special.
Bats don't really have an opposite. The Fairy is currently the only unit that come close to an opposite.
In Monster Wars, Bats are what vampires morph into for their special.
They appear in Endless Waves starting in Sun Kingdom. On level 25 of Frostburn Endless Waves you even fight him as a boss (a huge bat surrounded by minibats).