Just as the title says I'm going to give a template of some Bat villains and you tell us what your favourite story for each is. Comics only, Let's go
KILLER CROC. Batman 471 requiem for a killer by Alan Grant and Norm Breyfogle. Grant made Croc a villain some actual pathos rather than just some hired muscle or an actual giant monster.
TWO FACE. I'd say the long Halloween but since it involves many villains I'll go with Half a life from Gotham central. Greg Rucka really nailed the relationship with Montoya
MR FREEZE. Slim pickings in the comic world......maybe Snow?
CLAYFACE. The Mud Pack
MAD HATTER. Probably madness from Haunted Knight by Loeb and Sale
RIDDLER. Dark Knight Dark City by Pete Milligan.
POISON IVY. Think it was called A Walk In The Park. It was during No man's land.
These are off the top of my head. What have you guys got?