A combat specced battleship flagship with escorts will do it. Enemy battleships should fall to your own - you can supplement yourself with strike fighters. Even a modest carrier wing will add punch to a fleet. Dominators make for good escorts - they have a good opportunistic missile offense if loaded with Harpoons, good PD, decent guns, are tough enough not to die quickly if they run into trouble, and aren't fast enough to get annoyingly in front!! (Honestly Dominators are just super solid and having 2 watching your back makes for a powerful battlegroup.)
In my experience, dedicated PD boats don't work, because the truly best way to kill fighters is to kill carriers. You need enough DAKKA to blow apart incoming fighters and bomber strikes, but then enough main guns to quickly kill the vulnerable carriers. Both the Paragon and Onslaught achieve this naturally, though Paragon is slow enough that I wouldn't use it for carrier hunting. Conquest I like to have flaks in the side mediums for that purpose (and some people like 1 sided designs - I've played with them but like dual sided better).
Having allied ships built with anti-fighter in mind - not dedicated anti-fighter, but at least decent capabilities - is the real trick. Fighters focusing down a target have a massive advantage: they have flares and a synchronized attack. But all the OTHER ships in your fleet can tear them a new one on the way in and out much easier. Eagles with 2 phase lances (3 is a bit too flux heavy, unfortunately) in the medium energies and kinetics in the ballistics are truly excellent for swatting down wings, especially when part of a fleet. For longer ranged interdiction, throwing up a Tac laser net can be good, though I often don't bother (Tactical lasers + IPDAI + turret gyros, preferably several on multiple ships). The long ranged Hammerhead (2 HVD + 4 IPDAI tacs) gives up some of the raw power of normal Hammerheads, but is a pretty darn potent support ship.
Its not really worth using most frigates in a large pitched battle like this. Specialty and high performance still work - Omens are lovely little bug zappers, and Monitors and Tempests also have a place.
