The largest single battle between whites and Native Americans that is well documented with a reliable order of battle for both sides is the Battle of Fallen Timbers on August 20th 1794. This battle was fought about 32 kilometers south of Toledo Ohio on ground chosen by the Western Indian Confederacy. A tornado had cut a swath through the forest of northwestern Ohio, on both sides of the Maumee river. This provided the natives with ready made breast works and was thought to be a fortified position to hold off the US Army led by "Mad" Anthony Wayne. General Wayne won his nickname during the Revolutionary war, but he did nothing rash or "mad" during the 1794 campaign. Indeed, he conducted a methodical campaign that won the Old North West for the United States. In 1790 and 1791 the Shawnee and their allies defeated smaller US Armies that were led by Generals Harmer and St. Clair. The 1791 campaign ended abruptly when St. Clair's army lost 800 men in a bloody ambush by an undetermined number of native Americans.
George Washington got Congress to raise 5000 troops and appointed "Mad" Anthony Wayne to lead this army. Starting out from Fort Washington, modern Cincinatti, Wayne trained his troops hard for more than a year. Then began a methodical advance up what is now the western border of the state of ohio. Every twenty miles, the army would stop and build a fort. they also built a high quality road that was intended to link the Ohio river valley to the western end of Lake Erie. By the time this army got to the area where the Battle of Fallen Timbers was fought, there were 2000 professional US Army troops and approximately 1000 Indian scouts and militia from Kentucky and Virginia. They outflanked the line of fallen timber to the east and won this battle rather quickly.
The Western Indian Confederacy had approximately 1500 warriors of the field for this battle. it was a multi tribal army, with the Shawnees led by Wayapiersenwah (Blue Jacket) and the Miamis, led by Michikinikwa (Little Turtle) making up the bulk of this army. There were also native American warriors from the Delaware, Wyandot, Ojibwas, Ottawa. Potawatomi and Mingo nations. There was also one company of Canadian militia led by Alexander McKilop that fought with the Western Confederacy at this battle. The Battle of Fallen Timbers was a quick battle, it lasted less than two hours.
Twenty years earlier, the Shawnee leader Cornstalk led a smaller Native American coalition of three hundred to five hundred warriors on an attack against some 1000 Virginian militia in the Battle of Point Pleasant. This battle was fought at the mouth of the Kanawa river, just across the Ohio river from the south eastern corner of what is now the state of Ohio. This battle was an all day affair that lasted at least ten hours, before the Native Americans retreated.
Both of these battles are well documented, but there is an earlier example of battles between Europeans and Native Americans that may have been even larger. Hernando Desoto and his entrada through what is now the Deep South of the United States and the lower Mississippi valley was basically a four year long running battle. After Desoto died, the Spanish retreated down the Mississippi river and were pursued by very large native American forces on several occasions. The four surviving chronicles of Desotos' expedition do not agree of the size of the Indian armies they encountered or even give a clear cut account of any specific battle, but Charles Mann's book 1491 says these accounts should no longer be dismissed. The Spanish were probably not over inflating the number of Native Americans that chased them away.
Sources: "The Shawnees and the War for America" by Colin Calloway
"Blue Jacket: War Chief of the Shawnees" by John Bennett
"A Spirited Resistance: The North American Struggle for Unity 1745-1815" by Gregory Evans Dowd