It turns out that Google Books has already digitized the "Dangerous Women" anthology which includes The Princess and the Queen. If you google "Dangerous Women" with proper names from the narrative, excerpts pop up on google search which shouldn't be publicly available yet.

One of these does confirm that dear God, the Dornish actually managed to kill Meraxes.

"Some claimed a crossbowman put an iron bolt through his eye, but this version seems suspiciously similar to the way Meraxes met her end, long ago in Dorne." [1]

So yes, Meraxes was killed by sustained crossbow fire which managed to penetrate its eyes. Crossbows have greater force behind them than longbows. Also, note that this confirms that historians consider Meraxes to be female: dragons actually shift gender as the needs of the species require (like certain kinds of amphibians); later generations thought this was a myth, though others debated that it was not. The point is that the Maester allegedly writing The Princess and the Queen doesn't think dragons can switch gender; so their only basis for calling a dragon "she" is the ones who are confirmed to have laid eggs. Which is good: I'd have been worried if ALL subsequent dragons were the progeny of only Vhagar and Balerion. Still...crud, the Dornish. It's like taking down a living god.--The Dragon Demands (talk) 08:46, November 1, 2013 (UTC)

Naturally. Sandserpent (talk) 19:38, November 3, 2013 (UTC)
[Shaking my fist] Fire cannot kill a dragon! --The Dragon Demands (talk) 19:51, November 3, 2013 (UTC)
But apparently a crossbow bolt through the brain can... I mean, if anyone was to fell a dragon it would be the Dornish! Sandserpent (talk) 20:10, November 3, 2013 (UTC)