Spent much of the game trying to play catch-up when the enemy responded to the one Scout I sent to a relic with over a dozen fighters - resulting in them having significantly higher resources throughout the game. Putting what I had into a Heavy Cruiser, some frigates, and a couple dozen strike craft. My fleet hit just as an enemy attack force was leaving sensor range; rather than pull back to deal with it, I gambled on beating their Flagship before they could pose a threat, and I was building extra ships at my Mothership anyway. It paid off, though I lost nearly all the fighters to a Missile Destroyer, and I had to pull the frigates back, leaving the Heavy Cruiser to finish off their Flagship and force a carrier to jump away(postgame stats suggest it exploded as well).
Though their Flagship was gone, they had a large force near my Mothership and Carrier, and the ships I had there were all strike craft and damaged frigates - and their force was mostly Multi-Gun Corvettes and Ion and Assault Frigates(with Field Frigates protecting them). I had to jump away the main ships, leaving behind the Resource Collectors to buy time. It worked, and with a few hit-and-run maneuvers, the Heavy Cruiser, joined by a freshly-built one and some Heavy Corvettes, broke apart the bulk of the fleet, and destroyed another enemy Carrier. The good news is, that without their Flagship, I needn't worry about any new Carriers or Destroyers.
With one Carrier left(found via probe, confirmed with sensor array), I started to build my fleet, and made an organized attack. The first fighter crafts did a strafing run on the Carrier, then pulled away to deal with their defending bombers, the H-Corvettes targeted their MG-Corvettes, the Assault Frigates attacked their frigates, and the Cruisers tore the Carrier to pieces. While I saw another enemy group going for my Mothership, the destruction of their last build-ship was declared a victory.