Guess I got lucky on this one?
When I first got the mission, I couldn't go back to where he was first reported because I had just started a contract which brought me to the other side of the galaxy. On my way back to the first reported sighting many, many jumps later I got the dreaded yet somehow "countrified" statement "Yep, he had a galactic hyperdrive fitted here. Used it too."
I jumped to Galaxy 2 and followed the trail. Eventually I got the "If you really want to fight him, he's at..." message.
I had read this thread and realized I'd need fuel to stay up with him, but the final jump was a long one and I had no fuel left. I figured I'd just jump in to see how rough this guy was.
Sure enough, about 10 seconds after I jump in, he appears (oddly, the first time, he seemed to fire at me while I was jumping, damaging my Advanced Space Compass). The second time I jumped I did notice a graphical aberration but no damage.
He locks onto me, I get him in my sights, and blast him, scoring 8-10 successive hits. He starts shooting sparks and I hit him with one more barrage. He fires a missile or two and explodes. One of the missiles must have been ECM hardened and hits, but that's it. I've fought Pythons who were harder...
Anyway the chase was fun and I'm pleased that the combat wasn't impossible, but it was definitely not very hard. I was expecting a protracted chase with the fuel injectors on or very strong shields.
I'm not complaining, as I'm now Dangerous status and 5000 credits richer, but this thread oversells it a bit, at least in my case. Maybe I damaged his fuel injectors? Or maybe I'm just very good?

(doubtful)