I've already shared this on a few reddit subs but I thought it'll be cool to share here as well. This was all found while reading the new Necron 9th Edition Codex.
Pg. 27
The mirth of all cruel things was Nyadra'zatha, who was called the Burning One, Immolating Glee and the Breath of the Infinite Pit. All things were its kindling for its will was the searing that blackened the strands of aeons, and its ravenous touch no thing of the real nor the Echo-realm might endure. It was the pyre of the labyrinth the torch of the ziggurats lost, the reaping winds of ember-blight. How came that thing unto its end no records speaks, but that a single etching upon a single wall upon a single world shows the Silent Lord himself laying the spear unto its molten heart.
Extract from Aeldari lore, the Book of Mournful Night...
Pg. 31
Szarekh's dais is empowered by a caged shard of Nyadra'zatha himself, while the Silent King's mantle is formed from the C'tan's flensed Necrodermis. It is the Burning One's own fire hat Szarekh amplifies through his regal Sceptre of Eternal Glory....
So while I don't think the Silent King necessarily soloed the C'tan Nyadra'zatha, partly because that's a bit too insane a feat for a single character in
40K, I think it's safe to assume he did deliver the final blow that either broke it into shards or weakened it enough to be broken into shards.