I don't claim to be an expert on the subject, so please bear with me on that! The sources don't appear to support the idea that William was without equal as a cavalryman and a fighter. They do however support the idea that he was a ferocious battle commander and a more than able warrior.

There are numerous examples and quotes from different events, predominantly from his early years and challenges in the initial rebellions against him, that describe how he was an able warrior. The earliest that I could find in my brief search was how 'The king [Henry of France] and the duke [William], undaunted by their violent attacks, went into action [Battle of Val-es-Dunes, 1047] with a counter charge of soldiers and inflicted such slaughter upon them that those who were not slain by the sword, were stricken by the fear of God and swallowed in their flight by the River Orne' (Gesta, p.123). Additionally, he is repeatedly described as 'flourishing in the strength of his youth' (Gesta, p.129) while also having, by this point, put down a major rebellion from his cousin, Guy. Of the same battle in 1047, a contemporary historian, Peter Rex, attributes the death of a knight from Bayeux, to William, and describes how the man, 'by the name of Hardrez, known among the militia of de Briquessart for his strength and audacity, and [William] struck him such a blow with his sword that he pierced his neck "between throat and chin"' (Peter Rex, William the Conqueror, The Bastard of Normandy, p.48). But, there is no clear indication that this was because William was the superlative warrior, indeed it could have been a fluke accident. But that is speculation.

He was repeatedly at war from 1047 (when he was no longer under the rule of his guardians) all the way through to his death, be it rebellions, fighting off invasions or initiating his own, and I believe that this is why he had such a reputation as a fighter, more because of his commanding abilities than his actual combat abilities. He certainly wasn't as renown as, say, William Marshall or Richard the Lionheart for his martial skill.

I hope that this has been of some use to you, apologies for the brevity and lack of information, I only had two books to hand. I can try and find some more information for you if it helps, but it may take a few days as I am away at the moment!

The collection of primary sources that I am using are 'The Gesta Normannorum Ducum of William of Jumieges, Orderic Vitalis and Robert of Torigni', Volume 2. It was translated by Elisabeth Van Houts.

Secondary: William the Conqueror, The Bastard of Normandy, Peter Rex.