A detailed description of that not-so-cordial first encounter can be found in Mourt’s Relation: a Journal of the Pilgrims at Plymouth 1622.
"By their noise we could not guess that they were less than thirty or forty, though some thought that they were many more. Yet in the dark of the morning we could not so well discern them among the trees, as they could see us by our fireside. We took up eighteen of their arrows which we have sent to England by Master Jones, some whereof were headed with brass, others with harts' horn, and others with eagles' claws. Many more no doubt were shot, for these we found were almost covered with leaves; yet, by the especial providence of God, none of them either hit or hurt us though many came close by us and on every side of us, and some coats which hung up in our barricade were shot through and through.After leaving the area of First Encounter, the Mayflower continued along the coast, eventually landing at Plymouth. The full text of Mourt’s Relation, along with a host of other primary source materials relating to Plymouth Colony, can be found at The Plymouth Colony Archive Project at the University of Virginia. That project is a collection of fully searchable texts. Among those texts are; court records, colony laws, seventeenth century journals and memoirs, probate inventories, wills, town plans, maps, and fort plans; research and seminar analyses of numerous topics; biographical profiles of selected colonists; and architectural, archaeological and material culture studies.
So after we had given God thanks for our deliverance, we took our shallop and went on our journey, and called this place, The First Encounter."
The drawing depicting the First Encounter comes from King Philip, by John S. C. (John Stevens Cabot) Abbott. Written in the mid-19th century, that book is available full-text from Project Gutenberg.