Do the research that pops up.. Without that it's pretty much impossible to beat...

What Ruin said. Send the 3 ships to find out whats going on. Once you do, as you know the swarm fleet will spawn but so will a situation that requires you to do 1 yr of research on it. Research that for 1 yr, and you will then get a boost to swarm fleet damage which makes them simple to kill. What I also do, is when I know which system the swarm fleet will start in, I take control of it and build at least a t1 star base to help slow the fleet down. This way they dont hit alot of your systems before the tech is researched.

I missed you saying you had done the research... You're probably focusing too heavily on large ships, then...

Large ships should only be the "anchor" of your fleets... The bulk should be smaller ships...

I know it seems counter-intuitive, but small ships have high evasion, giving them alot of survivability, and should they get destroyed, they're cheap to replace... Additionally, 2-3 Frigates have about as much fire power as a Cruiser, require less fleet points (meaning even more of them can be deployed) and you can afford to replace a couple when lost far more readily, than losing a Cruiser...

You're probably getting overwhelmed by the sheer number of ships in the swarm, and have too many large ships of your own...

Fleet values are a little misleading in Stellaris, as small-ship only fleets can decimate large ship fleets easily, yet will have much smaller fleet values, and I find it's even worse in STNH...

Oh, and also got for accuracy and tracking over damage buffs... Doing an extra few % of damage is pointless if you're not hitting the target, whilst that extra hit bonus will be far more noticeable...

Had similar issue, I personally think it might be bugged as I had the 200% research come up a couple more times after the initial one had completed (the two times I reengaged) and had double the fleet value of the swarm and still got thrashed. Trill fleet finally came to the system they were loitering in and finished it.

With the latest changes it seems that it dosn't make much sense to build larger ships as soon as you have access to the UFP fighters. Shuttles don't seem to do the trick, only the fighters.