Before my multi-reply - I want to state that I am enjoying this discussion. I know it's adversarial, but I don't mean for it to be antagonistic. That said, have at you!!!
The full quote from the Letter says that in her youth she "was then of Amazonian disposition, and bound up her hair when taking parts in athletic feats". So the idea that this simply means tall or strong is already insufficent - it specifically refers to her character, and her propensity for physical feats.
I mean, what you said about the quote "Amazonian disposition" is exactly how *I* interpret it - so, this doesn't support your point, but undermines it. I am the one who takes that to mean she's a strong person, & probably tall. So, I'll accept "strong" as referring to her
character &/or
will as well. You're making my point for me. Thank you. It in no way implies she's was a warrior
We are further told (Shibboleth of Feanor) that "she grew to be tall beyond the measures even of the women of the Noldor, she was strong of body, mind and will, a match for both the loremasters and the athletes of the Eldar in the days of their youth." (so we know it wasn't just that she liked sport, it was that she was a match for any Noldor athlete in physical prowess. That's canon.
Yep. Still an awesome badass. No mention of being a soldier.
The Shibboleth also tells us that her mother-name (a name that is given some time after birth, often years, and is supposed to carry the character of the child was Nerwen, which means Man-Maiden. Or, as we know the term better, Tomboy.
As you noted, we know that she is variously listed as taking places in multiple battles, most notably Alqualonde. There are no mentions or implications made in those texts (unlike the breaking of Dol Guldur) that she was fighting in those battles with magic, and while it's true she did so at Dol Guldur, it's also explicitly noted first age and second age Galadriel was a very different person than late Third Age Galadriel, so it doesn't have much indicative value.
Granted, no point for either of our sides. Although I'll point out that "Tomboy" <> "Warrior". She's awesome. One does not need to be a warrior to be awesome. She's still the greatest Sorcerer in the Three Ages.
Moreover, we know of other high Noldor who were gifted in magic: it never stopped them from also being formiddable warriors. The magic/physical prowess opposition is not really present in Tolkien (see also, Gandalf), where the distinction is more between warriors and healers (I believe that one is from Morgoth's Ring), where the taking of lives dim one's talent at saving lives. Elrond, for example, notably abandoned the way of the warrior to focus on the ways of the healer at some point in his life (and is noted as one of the great Middle Earth healers), but Galadriel's healing is never much discussed.
Elrond is not a great warrior either. But that's a separate topic. But, current discussion: this is irrelevant - some members of X were also Y does not mean all X are Y.
Taken altogether, we know she took part in battles (with no special indication to say she didn't fight physically). We know she was inclined to physical action. We know she had the physical prowess to back it up. And we know her being a warrior does not conflict with her attested skill at magic. At this point, these add up to a pretty solid case for Galadriel's fighting to have been at least in part physical, and it's the "not a warrior" side that must make a case for why not.
"(with no special indication to say she didn't fight physically)" - <- this. She just as likely, more likely is my point, took part in battles as one of the greatest sorcerers ever. There is no evidence she
ever wielded a sword, even once. That it "did not conflict" is not enough to go on. It did not conflict that she transformed into a Dragon & slaughtered her enemies - not good enough to justify portraying that as something that happened, though, IMO.
