Tweedledum and Tweedledee

Cousins with an uncanny resemblance to each other, Deever and Dumfree Tweed both shared criminal leanings and a fixation on Lewis Carroll's Alice in Wonderland. Teaming up, they've modelled themselves after Tweedledee and Tweedledum  from that book, planning often outrageous, absurdist schemes to trap the Batman.

Arkham Origins Incident
It is unknown if the Tweeds had started their criminal career and if they've encountered Batman at least once at this point.

Between Arkham Origins and Assault on Arkham Incident
Around this was when the cousins started there criminal careers.

Assault on Arkham Incident
Tweedledum and Tweedledee were not present in Batman: Assault on Arkham.

Road to Arkham Incident
When Batman brought Joker back to Arkham Asylum, Tweedledum and Tweedledee were playing at the seesaw close to the entrance to island. They escaped the island once Batman drove through the gates, leaving their hats behind in all the hurry.

Arkham Asylum Incident
Though they had escaped Arkham, Riddler had set a riddle involving them. When scanning the seesaw, the riddle "Tweedledum and Tweedledee SAW it. Can you SEE it?" will be solved and their bio can be unlocked.

Between Arkham Asylum and Arkham City Incident
After the shut down of Arkham Asylum, the cousins attempted to leave Gotham but didn't know that they were being monitored by Hugo Strange (and, incidentally, The Riddler), who had the villains transferred to Arkham City when they were apprehended by TYGER at a checkpoint on the edge of the city.

Arkham City Incident
During the Arkham City crisis, Tweedledum and Tweedledee were working under the Wonderland Gang. They disguised themselves by wearing the riot gear of the GCPD, using it to lure Vicki Vale into a false sense of security before knocking her out and then bringing her to the Mad Hatter to act as one of several Alices that the Hatter forced to attend a Tea Party.

Later they were on guard at the Hat Shop, guarding the Mad Hatter's event. Batman quickly dropped down from the roof and took down both cousins before proceeding into the shop to disrupt Hatter's event.

After Arkham City Incident
Several nights after the death of the Joker at around 4 AM, Tweedledum and Tweedledee were caught up in a melee with the Batman within the walls of Arkham City. Tweedledum became confused as he thought Batman was calling them "Alfred" not knowing he was on the intercom talking to his butler. Batman mockingly replied that he couldn't bring himself to call a grown man "Tweedledum" right before he used his grapple gun to knock Tweedledum out.

Before Arkham Knight Incident
After being hired by Penguin to steal the latest incarnation of the Batmobile, their failure led to their incarceration in Gotham City central holding. While there, the Arkham Knight fired three shots with a shotgun, in the holding cells that they and Tweedledie were being held in, one of them explicitly at one of the Tweedle cousins, indicating that all three are dead.

Tweedledum and Teedledee
Real Names: Deever and Dumfree

Batman's Datebase Profile
Deever & Dumfree

Dr. Penelope Young
Psychological Profile: The Tweed cousins obession with Alice's Adventures in Wonderland is similar to that of Jervis Tetch but unlike Tetch the Tweeds are not delusional so much as severely dependent on each other with a shared fixation on extreme roleplay. They know they are not Tweedledum and Tweedledee but none the less delight in acting like them. Their complex rhyming and compicated in jokes and prolong their treatment sessions but the intense aggression they show when separated hardly make things easier.

Additional Notes

It's difficult to believe they are cousins, as they could pass as identical twins. I suspect plastic surgery.

I avoid scheduling sessions with them on the same days I'm treating Tetch, as otherwise the nearly endless recitation of selections from Lewis Carroll would be enough to make even me question my sanity. Or at least my career choices.

Attributes

 * Obsession with Alice in Wonderland
 * Skilled criminal masterminds
 * Despite being cousins, could pass as identical twins