Will Arnett acknowledged that the raspy, whispery voice he used for Batman is the same voice he uses with his children when he's giving them important parenting information.
(at around 8 mins) Batman's line in the beginning action scene, "You want to get nuts? Let's get nuts!" is a reference to Batman (1989), where Michael Keaton's Bruce Wayne says this line to Jack Nicholson's Joker.
Bane's voice and accent in this movie is based on Tom Hardy's portrayal of Bane in The Dark Knight Rises (2012). The voice is done by Doug Benson, a stand up comedian and podcaster who has done his comedic impression on Hardy's Bane since The Dark Knight Rises (2012) was released. The directors were fans of Benson's podcast, and hired him based on that.
Batman's crazy laugh was voiced by director Chris McKay. It was originally a placeholder before Will Arnett's laugh was to be put in, but never ended up being changed.
Billy Dee Williams voiced the nefarious Two-Face in this movie. Williams portrayed Two-Face's "good" alter ego, Harvey Dent, in Batman (1989). He was very eager to also portray Two-Face, but did not get the chance to, due to Joel Schumacher taking over the franchise with Batman Forever (1995) and re-casting the role with Tommy Lee Jones.