Holding Dirt on somebody. Proof somebody did a bad act, and holding it over their head. Threatening to expose Dirty act in order to get money or something from the Dirty person.
Got the shit on somebody.
Blackmail.
A portmanteau word combining the words "Kompromat" and "Complicated". Kompromat - Russian term for compromising information leading to blackmail, and, "Complicated" - Consisting of many interconnecting parts or elements; intricate.