After watching so many Batman fights, I can't imagine controlling him without a lock-on system. Locking on prevents the character from turning around and exposing their back to the enemy as soon as the player tries to pull away from their attacks or gain space [1]. It allows two fighters to dance [2][3]. I would assign the lock-on to L1, as a hold function. The player would switch to the next closest target ahead (and back) both by pressing down the left stick, meaning the L3 button [4], and by letting go of L1 and quickly locking on again [5]. This system, called "Z-targeting," was common [6] before Demon's Souls and Dark Souls popularized [7] the R3 lock-on [8]. I prefer the older system because it's not a toggle, thanks to the button not actuating at the base of a tilting stick. Because it's so easy to keep the button depressed and the function is actively felt rather than only seen, the player is more aware that it is active and the ability to run backwards and sideways is just built in even when there is no target. This can make lining yourself up for things in the environment outside of combat a little bit easier. If you wanted to be really creative, you could even let the player move sideways between narrow walls without triggering the usual canned animation [9][10]. Ocarina of Time and later Zelda games HAD toggle options, and I always hated them [11]. I would NOT lock the camera behind Batman while the targeting system is active. [12] It cuts off too much visibility. You can't see what you back into. Using the jump button with the lock-on button would allow my player to perform a kind of dodge. However, to make them use as many of the fight mechanics as possible, have them heed the positions of their enemies and hopefully keep them moving, jumping to the side or backwards would not be effective against every attack or type of enemy.
[1] animated series scenes > animated_lock-on_1.mkv
[2] animated series scenes > dancing_(Legends_of_the_Dark_Knight).mkv
[3] Fury_(Justice_League).mkv
[4] Targeting_DMC3_A.mkv
[5] Targeting,_Zelda_A.mkv
[6] Targeting,_MGS3_B.mkv
[7] Demon's_Souls_targeting.mp4
[8] Elden_Ring_R3_targeting.mkv
[9] Targeting,_Zelda_B.mp4
[10] Rise_of_Tomb_Raider_canned_animation.mp4
[11] *Record the toggle option in menu of Wind Waker or Ocarina of Time*
[12] Elden_Ring_R3_targeting_lack_of_visibility.mkv