Cassandra is a princess of Troy from Greek mythology, most notably The Iliad. So what the heck is she doing here in our discussion of 12 Monkeys? Serving allusion duties, which these days is pretty much the main gig for mythological characters who aren't Thor or Hercules.
Dr. Railly references Cassandra in her book discussing the relationship between madness and apocalyptic visions. As she puts it:
DR. RAILLY: Cassandra, in Greek legend, was condemned to know the future but to be disbelieved when she foretold it. Hence, the agony of foreknowledge combined with the impotence to do anything about it.
When found in the mentally ill, this agony is called the "Cassandra Complex."
As you can likely guess, Cole and Cassandra have a lot in common, which makes for a fitting allusion. Cole warns that the world will be destroyed by a virus, and Cassandra warns the people of Troy that the Greeks will wreck some face in the war. Neither one is believed, and their respective worlds are destroyed as a result.
Both also suffer horrible fates. Cole is killed by police as he tries to stop Dr. Peters from boarding an airplane with the virus. During the fall of Troy, Cassandra is raped by Ajax, taken as a concubine by Agamemnon, and later murdered by Agamemnon's wife, Clytemnestra.
Cole has it rough, but he's got nothing on Cassandra in the fate department.
Although not mentioned by Dr. Railly, Cassandra also suffers from a type of madness. In the play Agamemnon, by Aeschylus, Cassandra's moments of prophecy are staged as fits of madness (source). Totally understandable, given that she was witnessing her own death. Similarly, Cole questions his own sanity given the knowledge he possesses.
Given how much they have in common, Cole and Cassandra should really get together and start a support group for characters from tragic stories. We know a couple kids from an island that could really use the therapeutic assist.