The following sentence is cited from a textbook called American English in Mind 4.
In other words, he ran 43 marathons in less than two months before he finished in great style and puring rain in London's Trafalgar Square.
What does in great style mean?
Since it's a marathon I would take it to mean that for the last part of the last (43rd) race he finished the last part "looking very good". If you've seen marathons you'll notice that people get extremely tired towards the very end of the race (typically starting around the 22'nd mile out of 26.2 miles), and as they get tired the way they run looks "poor". Imagine an elite athlete running only 400 meters at a (to him/her) medium speed; they will look very good. Nice posture, great strength and power. But at the end of a marathon - especially the 43rd one in only two months (!) - people tend to look not so great.
So the gist of this is that not only did he run very many marathons in a very short amount of time, but he also finished the last one looking great.