BEST NEW ENEMY: Big Sister (BioShock 2)
The outstanding opponent this time around is the incredibly strong Big Sister of the sequel to BioShock. If you thought Rapture threw some tough baddies your way the first time around, you were in for a surprise in BioShock 2. A far deadlier and more agile boss than the Big Daddies of the predecessor, these encounters (at least earlier in the game) necessitated a greater degree of caution and planning than their lumbering counterparts.
By the end of my second run through the original BioShock, Big Daddies were no longer very frightening, as I had learned to beat them to death with a pipe wrench, which denotes a degree of comfort. Bigger, stronger Big Daddies with more hit points wouldn't have been a game changer in BS2, which lead to the inclusion of their nimbler cousins. In the original, Big Daddies would be seen in the wild, making their rounds, escorting Little Sisters, ignoring the player, which enabled the player to observe and learn the route and plan accordingly.
Encounters with Big Sister followed a different pattern. After taking care of enough Little Sisters (one way or the other), Big Sister would come find you, wherever you were, to initiate the fight. She would then proceed to blast you with plasmids, drain your EVE with a giant needle, go fucking Maximum Spider on your ass, as well as generate telekinetic debris storms to deter you. Overall a much more harrowing experience.
This official final sketch by Colin Fix.
A runner up nod goes to the recurring boss Barthandelus from FFXIII.