By far the mightiest space monster one can encounter is the Guardian in the Orion system. With its superior weapons and defensive technologies against almost every threat he cannot be overwhelmed until fairly late mid-game.
A beam defense of 100 rules out beam weapons without computers from the highest tiers and its missile defense values baffle attacks with sheer numbers of missile carriers. Wearing it down in extended fights also doesn't work very well, since it can repair some inflicted damage every turn.
Fortunately there is one class of weapons that cannot be countered: Special Weapons. Usually, with decent research one can go for Plasma Web before turn 200. The special feature of Plasma Web is that it deals damage over time, which gets reduced every turn by 5, but only the sum of all simultaneously applied plasma webs. So it is wise to build two Titans packed with 13 Webs each and armor them so they can stand the first turn against the Guardian. Next, after the application of the plasma webs you just need to escape from the Guardian's weapons for some turns and let the Webs wear down the Guardian quickly without losses.
Another strategy using Special Weapons to destroy the Guardian early in the game is to employ Gyro Destabilizers. If your economy can afford to lose a few Battleships, a handful of them can quite easily take down the Guardian with Gyro Destabilizers. This is due to the fact that Gyro Destabilizers directly damage the Structure when used. These ships are also fairly useful for early attacks from Antares.
If your economy can handle losing some ships, six to eight cruisers with tritanium armor will also do. This is a trade every player should be willing to make since the technological goodies of Orion clearly outweigh some hundred PP.
You can also use around 9 destroyers on the Guardian. The trick is to drop his shields only for a sec and then ram in a 2x/MIRV/Emission Guidance/ECM/Fast/Hvy armored merculite. This usually kills The Guardian in one shot by blowing up his engine. The rest of the fleet uses MIRVed merculites without the EMG mod to get a hole in those frontal shields.
This can be done around turn 100 if you have chosen the right picks and focus your tech. The battleship you receive from Orion easily outmatches the rest of the game by far at this time. Choose your new enemies and show them your new battleship! It wipes out whole fleets at turn 100, AI or human opponent.
For a kill later in the game, plasma cannon works very well also.