the lord of the rings - How on (middle) earth did Eärendil kill a dragon as huge as Ancalagon?

We know that Ancalagon was killed by Earendil, but how exactly was he killed? Ancalagon was so incredibly massive and Earendil was just a dude in a ship with some Eagles.

This image ↓ isn't canon but it probably isn't far from Ancalagon's in-universe size description where he's said to have destroyed 3 giant volcanoes just by falling on them.

Answer

There is no canon answer to this. As you point out, literally the only description we have of this is that

Before the rising of the sun Eärendil slew Ancalagon the Black, the mightiest of the dragon-host, and cast him from the sky; and he fell upon the towers of Thangorodrim, and they were broken in his ruin.

(The Silmarillion, Chapter 24, "Of the Voyage of Eärendil and the War of Wrath")

However, consider the power of the Silmaril that Eärendil wore:

And the wise have said that it was by reason of the power of that holy jewel that they came in time to waters that no vessels save those of the Teleri had known; and they came to the Enchanted Isles and escaped their enchantment; and they came into the Shadowy Seas and passed their shadows, and they looked upon Tol Eressëa the Lonely Isle, but tarried not; and at the last they cast anchor in the Bay of Eldamar, and the Teleri saw the coming of that ship out of the East and they were amazed, gazing from afar upon the light of the Silmaril, and it was very great.

(The Silmarillion, Chapter 24, "Of the Voyage of Eärendil and the War of Wrath")

Further, this was the very Silmaril which Beren and Lúthien had taken from Morgoth, and which injured the wolf Carcharoth nearly to death:

Carcharoth looked upon that holy jewel and was not daunted, and the devouring spirit within him awoke to sudden fire; and gaping he took suddenly the hand within his jaws, and he bit it off at the wrist. Then swiftly all his inwards were filled with a flame of anguish, and the Silmaril seared his accursed flesh. ... Of all the terrors that came ever into Beleriand ere Angband's fall the madness of Carcharoth was the most dreadful; for the power of the Silmaril was hidden within him.

(The Silmarillion, Chapter 19, "Of Beren and Lúthien"; emphasis added)

Thus it is probably not beyond reason to believe that the power of the Silmaril aided Eärendil in some way, and perhaps even had some direct part in the death of Ancalagon. But we are never told in so many words.