The OP didn't include one of the best warriors just because she was a woman. Hmm. Intresting.
In Laws and Customs of the Eldar it is clearly stated all female
Elves could fight valiantly. See the essay in
Morgoth's Ring to find more. I quote a bit of it here: "indeed in dire straits or desperate defence, the nissi (
elf women) fought valiantly, and there was less difference in strenght and speed between elven-men and elven-women that had not borne child than is seen among mortals." The reason why they didn't fight more often is due to valuing their healing powers. Elves healing power gets lessened if they kill anyone, this is true for both male Elves and female Elves.
Anyway, to
Galadriel, the most badass girl.
"These two kinsfolk [Galadriel and Feanor], the greatest of the Eldar of
Valinor,(14) were unfriends for ever." "Who together with the greatest of all the Eldar,
Luthien Tinuviel, daughter of
Elu Thingol, are the chief matter of the legends and histories of the Elves." - Shibboleth of
Feanor
«Her mother-name was Nerwen (‘man-maiden’), and she grew to be tall beyond the measure even of the women of the
Noldor [193cm]; 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.» - Shibboleth of Feanor
«Nor were the 'loremasters' a seperate guild of gentle scribes, soon burned by the Orks of
Angband upon pyres of
books. They were mostly even as
Fëanor, the greatest,
kings, princes and warriors, such as
the valiant captains of
Gondolin, or
Finrod of
Nargothrond and Rodothir his kinsman and steward.» - [Shibboleth of Fëanor; Note 23]
"Galadriel, the only woman of the Noldor to stand that day tall and valiant among contending Princes" - Silmarillion
Tolkien describes high skilled official professional female warriors as 'Amazon':
“[Éowyn] was also not really a soldier or ‘amazon’, but like many brave women was capable of great military gallantry at a crisis.” - The Letters of JRR Tolkien, Letter #244
In an early draft
Eowyn was "a stern Amazon" who "goes as Amazon" to war. Clearly means she rode to war openly and as a real professional warrior. This idea about Eowyn was abandoned, as you can see.
"One of the strange practices spoken of was that many of their warriors were women, though few of these went abroad to fight in the great
battles. This custom was evidently ancient; for their chieftainess Haleth was a renowned Amazon with a picked bodyguard of women." - The Unfinished
Tales
"[Galadriel] was then of Amazon disposition and bound up her hair as a crown when taking part in athletic feats” - Tolkien Letter 348
Galadriel is a brave 'Amazon'.
“A sister they had, Galadriel, the fairest lady of the
house of Finwe, and the most valiant.” - Morgoth's Ring
So I think these are enough to understand how much of a capable warrior she was.
Now which battles she fought in?
First Kinslaying: "Even after the merciless assault upon the Teleri and the rape of their
ships, though she [Galadriel] fought fiercely against Fëanor in defence of her mother's kin, she did not turn back." - People of
Middle-earth, the Shibboleth of Feanor
The Battle of the Lammoth. As a leader in the
Flight of the Noldor and crossing the Helcaraxë, she must've still been a leader in this suprise attack which befell them after crossing the Helcaraxë. (In such crisis and desperate defence even the most devoted Elf healers fought)
The Second and Third Kinslayings: if Galadriel was in
Doriath and Sirion, then she must've participated in these battles. Christopher Tolkien argues and speculates that she naturally must've been there (a very valid guess if we are going by
Sindarin Celeborn versions).
The Fall of Eregion: "after Eregion's fall Celeborn led this migration [of the survivors of Eregion] to
Lórien, while Galadriel joined
Gil-galad in
Lindon; but elsewhere, in a writing contemporary with this, it is said explicitly that they both at that time "passed through
Moria with a considerable following of Noldorin exiles and dwelt for many years in Lórien." " - Unfinished Tales, History of Galadriel and Celeborn
The assault of
Sauron on Lindon: if you are going by the version where she escaped to Lindon, then yes. They were barely holding
the Grey Havens, they were desperately fighting in its defence. Not only Galadriel who was full Amazon and strongest woman and etc, but also many other women were needed in such dire straits and desperate defences.
The Battle of the Gwathlo and the Rescue of
Rivendell: Galadriel might have stayed back in Lindon. But it's hard to imagine that Galadriel went through the worst and deadliest parts of the war, but then didn't participate in the victory part, in the most satisfying part, in the easiest part.
I should mention, the gal who wanted to kill Feanor: “now she burned with desire to follow Fëanor with her anger to whatever lands he might come, and to thwart him in all ways that she could.” - SoF
The Last Alliance: unknown.
Here we enter Third Age when I highly doubt if Galadriel ever killed anyone anymore. I believe she had fully devoted herself in everything that is things-not-killing. But it's evident that she still fought, preferably with magic now. Also, to support these, we have a statement from Unfinished Tales that says in Third Age she was "unable of punitive action" but amazing in resistance. And also, the fact that Tolkien says Galadriel was Amazon BACK THEN, as in to imply she wasn't Amazon/warrior anymore.
The Second Siege of
Imladris: possible. IF she had already finished her
journeys of inquiry.
The rescue of
Lorien (not really a great battle or something, but it was still a rescue).
The clashing against Sauron in the Ride of
Eorl: in short, Sauron sent shadows of terror against the Riders of the North, but Galadriel drove back Sauron's sorcery with her mist. (Sauron was in a weakened form at that time, but still he was very powerful)
The Attack of the
White Council On
Dol Guldur where they drove back Sauron (yes the retreat was already planned, but he would've LOVED to crush his chief enemies, it's just he couldn't face so many of his powerful enemies, so he stuck with the plan)
The Three Assaults of Dol Guldur on Lorien: "Three times Lórien had been assailed from Dol Guldur, but besides the valour of the elven people of that land, the power that dwelt there was too great for any to overcome, unless Sauron had come there himself."
The Fall of Dol Guldur: "when the Shadow passed, Celeborn came forth and led the host of Lórien over
Anduin in many boats. They took Dol Guldur, and Galadriel threw down its
walls and laid bare its pits, and the forest was cleansed." (LOTR Appendix B)
Fingolfin was perhaps the best fighter, but Galadriel was far more efficient than him.
Glorfindel is a good efficient one too. But Galadriel played more "universal" and crucial roles.