Now, there were probably debates about this topic, but I am on the opinion that Hector Salamanca and Chuck McGill are two main overarching antagonists of the entire universe.
These two old men have caused almost every single event in the entire saga.
Hector Salamanca
Hector was one of the founding fathers of the Cartel, the patriarch of the Salamanca Family and he made Lalo, Tuco, the Twins and Gustavo Fring into the men who we saw them as in both shows.
He abused his nephews, into becoming ruthless and psychopathic criminals who absolutely care about nobody but the Salamanca Family with Lalo being the most dangerous out of them all.
Although he did it under Eladio's orders, but of course even if Eladio didn't even exist he probaly would've done it either way, but Hector killed Gus' boyfriend which made Gustavo into the cold and calculating man we see in BCS and BB. Now, Gus was already planning to become a kingpin, no doubt about that, but he probably would've been more merciful and far less cruel if Max didn't die.
The Salamanca vs Fring conflict has been the most influential and relevant conflict throughout both shows. This conflict alone caused the lives of numerous people, all because Hector shot Gus' boyfriend, while the Salamanca Family has been responsible for many more atrocities at the hands of his nephews whom were all trained by Hector himself.
However, this is but only the criminal side of the story, let's go to the legal side.
Chuck McGill
It's insane to think about the fact that without Chuck, there would be no Saul Goodman and Heisenberg's Empire wouldn't even exist.
Chuck's inability to forgive Jimmy and see past his brother's chicanerous antics of the past blinded him to the fact that Jimmy tried desperately hard to turn around his life. Jimmy genuinley tried to be a good guy in the beginning, however after HHM rejected him for the second time (thanks to Chuck, again) and realizing that Chuck was behind it all, made Jimmy slip back to his Slippin' Jimmy persona. After Chuck commited suicide after he lost everything, Jimmy slowly broke bad and created a whole new identity in the form of Saul Goodman.
At the same time, Saul teamed up with Mike on several occasions, in the end even hiring Mike as a private investigator and helping Mike's business with Gus (although Saul had no idea who Gus was untill Gustavo died).
How does it all lead to Heisenberg?
Well, both of them are indirectly responsible for Heisenberg. No, this is actually serious. The best way to understand this is to look at BCS seasons 5 and 6, along with Saul's debute episode in Breaking Bad "Better Call Saul."
As I mentioned previously, Hector made Lalo into the man he is and Chuck made Jimmy into Saul. Lalo and Saul meet in BCS season 5 for the first time, when Lalo needs Saul to save Domingo "Krazy-8" Molina from prison, which Saul actually succeeds in.
Lalo later calls Saul to help him avoid imprisonment and Saul eventually bails him out with 7 million dollars. This event made everyone whoever works at the court despise Saul, because they eventually realized that they literally allowed a psychopathic drug lord walk free without a problem and Saul helped him. However, this also earned new clients for Saul as many people in the criminal underworld heard about the story and hired Saul as their lawyer.
This later lead to Saul's business growing big, earning the reputation of Saul Goodman as the CRIMINAL lawyer in Breaking Bad, leading us to Jesse convincing Walt to hire Saul as their lawyer in season 2 which was the start of a chain reaction leading to the Rise and Fall of Heisenberg. Like Jimmy said in "Saul Gone":
"So yeah, I wasn't there when the meth was cook, I wasn't there when it was sold, I didn't witness any of the murders but I damn well knew it was happening! I was more than a willing participant, I was indispensible! I kept Walter White out of jail! I laundered his money, I lied for him, I conspired with him and I made MILLIONS! If he hadn't walked into my office that day, Walter White would've been dead or behind bars within a month... And Agent Schrader and Agent Gomez and whole lot of other people would still be alive... Fact is, Walter White couldn't have done it without me."
