You have to listen closely, but Giuliani explains the connection succinctly, beginning shortly after the 6:30 mark:
Giuliani traces this back to 2016 when, he states, Obama told the Ukrainians to gather dirt on Trump. Biden was Obama's "tsar" for Ukraine. Biden got the Ukrainian prosecutor fired who was investigating his son's corrupt connections--the prosecutor wouldn't play ball. He wanted to attack corruption on behalf of a sovereign Ukraine. Biden then appointed a prosecutor for Ukraine--there's no other way to put it. That prosecutor was one who would play ball with the Obama administration. The prosecutor then went to work doing the work of the Obama administration. That work was to arrange a successor administration to Obama's, headed by Hillary Clinton. To that end the prosecutor started by dismissing a case against an organization (funded by George Soros) that was manufacturing "information" about Trump and Paul Manafort and feeding it to the DNC, through the instrumentality of an FBI agent who now works for Soros.
Laura challenged Giuliani: Why are you doing this investigating instead of the FBI and DoJ? Rudy's response is telling. He directly attacks the FBI but stays away from DoJ and Barr:
Rudy: "We've lost the FBI and who knows what else."
Laura: "We can't lose the FBI. We have Bill Barr over at Justice. No way we're losing the FBI under Barr."
Rudy: "Their inability to investigate this is astounding. You know how this first came to me? It came to me from this very prominent investigator telling me, for one year they were trying to get this information [Ukraine collusion]. You ask me why I'm doing this? Because the FBI didn't do their job! ... I will show you the statements of five Ukrainians who will tell you, We desperately tried to get the information to the FBI and we were blocked by the [US] ambassador [to Ukraine] who eventually got fired."
This confirms to me that the Barr/Durham investigation is involved in this investigation in a major way, as commenter Unknown has also been maintaining.