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 as well as its missile defense values baffle attacks with sheer numbers of missile carriers. Wearing him down in extended fights also doesn't work very well, since he can repair some inflicted damage every turn.
But there is one class of weapons that cannot be countered: Special Weapons. Usually, with a 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 Guardians weapons for some turns and let the Webs wear down the Guardian quickly without losses.
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 do since the technological goodies of Orion clearly outweigh some hundred PP.