Villains who, although acting for primarily evil goals, have understandable reasons for their motives due to suffering; hence, the reader/viewer can sympathize with them. Most of these villains are not in full control of their actions/emotions due to them not being evil by choice, but instead by them being, for the most part, a victim of circumstance. This also applies to groups such as organizations or hostile species whose members were driven to villainy due to a tragedy.

These characters are often suffering from Posttraumatic stress disorder (PTSD) and can develop into delusional, insecure or egotistic villains because their experiences develop their beliefs into obsessions, twisting them to insanity.

There are three ways to declare a Tragic villain:

• A villain with a backstory that has caused them anger and depression, shaping them into destructive and hateful beings. However, the broken heart is what is causing their evil actions. Instead, they are forced upon a path of darkness and their past has caused them to become distrustful and misled. This can happen if the villain was a loner or became addicted, loses loved ones, gets bullied in childhood, was severely scarred and so on (e.g. Atrocitus, Tyrion Lannister  and Count Bleck).
• Protective villains who commit crimes to protect the ones they care about. They are only looking out for whoever they love or care for, but use extreme measures to do so; due to this, they are sometimes confronted by the heroes or even the people they protect, making it even more difficult to save them (e.g. Johnny Klebitz, Cersei Lannister and Walter White).
• Possessed or brainwashed characters who are either controlled or corrupted by some kind of evil presence. Therefore, they are not willingly evil, but are manipulated by the power that is controlling them (e.g. Cujo, Gollum, Arthas and Ice King).

/!\ However, Pure Evil villains CAN NEVER fall under Tragic.

Either their "tragedy" would be extremely and outrageously logic-defying to be realistic, or they'd simply use it as an excuse to justify themselves and nothing more. Through their evil acts and by having no empathy, the Pure Evil villain manages to destroy their own innocence and as a result, the villain is no longer sympathetic.

Even if they are given a reason for doing what they are doing that involves a traumatic experience in their lives, they are FAR PAST tragedy due to their unforgivably horrendous actions (as seen in the cases of Scar, Johan Liebert, Ramsay Bolton, Voldemort, Arcturus Mengsk, Sauron, Joffrey Baratheon, Moff Tarkin, Koba, Lots-o'-Huggin' Bear, Isaac Ray Peram Westcott, Dio Brando, Freddy Krueger, Phasma, Emperor Ganishka, Infinite, Zoom, Milady de Winter, Light Yagami, Adam Taurus, Herrscher of the Void, Michael Myers, Drago Bludvist, Gul`dan, Ultraman Belial, Sheev Palpatine, Evolt, Syndrome, Frank Underwood and many versions of Carnage and the Joker).

Most of their excuses are just what they deserved; some even fake at least one tragedy occurred on them. For example, Jagi's "tragedy" was that his younger brother Kenshiro exiled Jagi from the Hokuto family after disfiguring his face. Jagi does not hold up as tragic as this was a response to Jagi trying to murder Kenshiro.

Also, DO NOT add certain characters like these, even if they are not Pure Evil:

• Villains who committed unforgivable crimes and have crossed the Moral Event Horizon - sometimes more than once - only due to a MERE EXCUSE which is FAR TOO PETTY to be counted as tragedy, and their crimes were too horrible that even their excuse or traumatic experience doesn't justify their actions, no matter how "sad" their experience seems. Nigel of Rio is an example of this as he rebelled against pretty birds just because he used to be a big animal star but was later was blindsided by a green parakeet named Petricious.
• Villains who faked a tragedy, or rather brought the so-called "tragedy" (no matter how sad it seemed) on themselves but blamed or framed others for it. 
• Villains who merely has an ironic defeat (like being betrayed by people they trusted) but had no tragic backstory to begin with. Naria is an example.

This category is for characters whose tragedy is not only TRUE and LEGITIMATE, but STILL holds up even after they've crossed the Moral Event Horizon.

Many of these characters are Fallen Heroes.