It seems to be generally understood (see the Tolkien Gateway and LOTR wiki articles) that:
In the Battle of Dagorlad, Oropher's company fought valiantly but he was slain with the greater part of his people when he, with King Amdír and his warriors, called an early charge upon the enemy, without orders from the Noldorin High-King Gil-galad.
But the chief source reads like this: .
The Silvan Elves were hardy and valiant, but ill-equipped with armour or weapons in comparison with the Eldar of the West; also they were independent, and not disposed to place themselves under the supreme command of Gil-galad. Their losses were thus more grievous than they need have been, even in that terrible war. Malgalad and more than half his following perished in the great battle of the Dagorlad, being cut off from the main host and driven into the Dead Marshes. Oropher was slain in the first assault upon Mordor, rushing forward at the head of his most doughty warriors before Gil-galad had given the signal for the advance.
[↑ J.R.R. Tolkien, Christopher Tolkien (ed.), Unfinished Tales, "The History of Galadriel and Celeborn", "Amroth and Nimrodel", Appendix B]
Though it is somewhat vague, to me it seems to refer to two separate incidents: One when Malgalad/Amdír either though ill luck, carelessness or bad coordination with the High King was cut of and slain in the Marshes, and a different one, when Oropher and his Mirkwood forces took unnecessary casualties "in the first assault upon Mordor", which can quite possibly mean that after the victory in the field, they were the first to try to enter Mordor proper (by charging at the Black Gate)
Even when Mordor here is taken to refer to the Host of Mordor, the order of the sentences is queer for the traditional interpretation: The separation of the Lórien forces would have been a consequence of their rash assault together with the Mirkwood Silvan, so either the statement about Amdír would have to follow that which is about Oropher, or connected to it by a "for" or "because", with the latter part explaining that they charged together.
Is it therefore possible that the two Woodland Kings had their armies decimated and their lives lost in two separate incident of miscoordination and wanton heroism in the War of the Last Alliance?