There's no way the GTVA can beat the Shivans if you're trying to take a "realistic" approach on your campaign (or just your point of view). But if you're trying to make your campaign really cool with a sense of victory, you always have the GTVA build 20 GTBS Archangel class ships in 2 years and have them defeat the Shivans. Again.
The Shivans have superior ships and weapons, but they just decide to throw everything at the GTVA mindlessly. Why? They don't care. They have 10000 destroyers, who cares if the SD Nebiros and the SD Beast go down? But the GTVA, they have something to worry about. They probably have about 20-30 destroyers, so if the GTD Messana and the GTD Aeneas go down, then it's a big loss for them. The GTVA have better tactics and win some of the battles, but there's NO WAY they can win the war against a species that has been wiping out entire civilizations for more than 8,000 years. In addition, if the Shivans were Derek smart enough (or cared enough for that matter) to cut their losses, they would use better tactics, and beat the GTVA's asses. But they aren't smart enough (or don't care enough) to do that so they just sacrifice thirty bomber wings but eventually, they will win the battle against an exhausted enemy battlegroup.
The GTVA CAN NOT beat the Shivans. Why? The Shivans have 80 ****ing Sathanes, what's to say they don't have more? Or something bigger? The GTVA are two species which have been spacefaring for at the most 100 years. The Shivans have been spacefaring and have seen combat in space for 8,000 frakking years. The Shivans might have a bit of a hard time defeating the GTVA, yes, the GTVA will put up one helluva fight before goin' down. But the Shivans will ultimately win, there's no other conclusion that is realistically possible.