Basically you need to start drawing lines across the map and try to get into a position where you've got a much better income than him/them.  You need to get just as dug in as him, and either wait for him to toss his fleet away trying to attack you or start building disposable fleets to suicide into his defenses before you bring your main fleet in.

I could be wrong, though, since I usually don't play against people.

It really comes down to last resort. The Ragnarok can kill a SB pretty quick but if the guy knows what he is doing, you will take grievous losses before he uses last resort.  I even killed him before he got Last resort off with Overcharge and snipe in one system.  

Once you crack the left nut, the right one is a lot easier to deal with.  Although waiting for reinforcements is usually necessary as Last resorts range is larger than Orgrov's without an Akkan.  Having Bombers is very necessary to deal with that one feature. Bomber spam has killed more than one SB after my fleet was wiped out.

The Ankylon can deal with this problem a whole lot better. Even with Upgraded last resort wont kill a fleet an Ankylon is defending. Although the slower nature of damage gives the person pushing the button a lot more freedom to choose when to push it.

Using rebel alliance to send in a ton of fodder to clear mines and tie up the SB has worked pretty well too. Also the pirate main fleet will move to support you if they are still around.  2 titans works enormously well, even if the other one was AI controlled.  My Ragnarok and an Ankylon goes through an opposing team mate super fast with very little down time.

What I do is I build a large corvett fleet (the only use i have for them) and have them blow up every single mine they can after that I send in a Large fleet with about 6 or 7 cap ships with nothing but lrms and garudas they will draw the fire then i send in the rest with my titan and orgarovs. since the titan is a moving cannon and starbase i use it to defend the ogarovs focusing on the right while the other fleet focuses on the left by that time the orgarovs have finished 1 starbase and the other is still there beating it out against my fleet i send them over to finish it off then use them to attack the buildings. After that you get the idea. Thats just my strategy ive used it against humans too and it works you just have to play smart.