Tiberius worked for the Triumvirate
Both he and the trio share Roman theme naming, and it would fit the theme of the Triumvirate being the Big Bad in the Contra universe, as said in Shattered Soldier. They are said to have lived, and manipulated humanity, for hundreds of years, doing so from shadows, so a figure head being seemingly the leader, and doing all the conquering, would make sense. Tiberius' Commonwealth would be just another of the Triumvate projects to size total control over the world. The Triumvirate had contact with Moirai technlogy and remains before 2627
The Celestial Imperator and Cerberus are products of research over an another, earlier discovery of an Alien Cell, as are Tiberius' transformations into Tiberius Augustus, and Tiberius Invictus. Alternately, The Celestial Imperator is a clone of a member of the Moirai species. Bahamut had a good reason for a Face–Heel Turn
Going with the above theories, he discovered that the Triumvirate was the real power behind Tiberius, and after the uprising, still controlled the majority of the world. He wanted to reveal the Triumvirate plans and existence, and end their century long rule in a new uprising. But the trio slandered him, framing him into war crimes he didn't commit, destroying his reputation, and credibility. Bahamut had to go into hiding, getting every possible resource and power needed to fight the Triumvirate, using more and more amoral methods, till he became not much better than the Triumvirate. Bahamut is Bill Rizer
Both Bahamut and Bill Rizer look like Arnold Schwarzenegger, and even one of the alternate outfits resemble Bill. Gameplay wise, Bahamut does pretty much like Bill Rizer of other Contra games. If Bahamut in Hard Corps: Uprising isn't the same person as Colonel Bahamut in Contra: Hard Corps, he would be the same person as Bill Rizer.Retconning Bahamut and Mandrake's friendship in Uprising to the development of Lucia in Shattered Soldier, Bill could be a good old friend to Dr. Mandrake.
Leviathan is Lance Bean
Leviathan and Bahamut is like Lance Bean and Bill Rizer. Also, Leviathan had a similar role to Lance in Shattered Soldier. Leviathan also has a similar length of hair to Lance. Going with the above theories, Leviathan could have been escaped the grip of death, pulled an Unexplained Recovery Heel–Face Turn, and joined Bahamut (Bill Rizer) in the events of the original Contra, before became a Tragic Monster in Shattered Soldier.