Did valiantly: means that Saul “fought bravely” (New American Bible), that is, he showed great courage in battle.
Smote may mean either “killed” or “defeated.” But in this context the latter seems more likely.
The Amalekites, first mentioned in Gen 14.7, were a nomadic tribe descended from Esau. They roamed the desert south of Judah, and there was strong animosity between them and the people of Israel. For Saul’s defeat of the Amalekites, see 15.1-9. The Hebrew here says “Amalek” (so New American Bible, Fox), but the context clearly shows the reference is to the Amalekites, as nearly all translations clearly indicate (see the additional comments on 15.2). It is not clear why Good News Translation says “even the people of Amalek.”
The hands of: on the metaphorical use of hands, see 4.8.
Who plundered them: that is, who had previously attacked the Israelites and taken their belongings. New Jerusalem Bible correctly focuses on the fact that this was something in the past: “who used to pillage them.”
Quoted with permission from Omanson, Roger L. and Ellington, John E. A Handbook on the First and Second Books of Samuel, Volume 1. (UBS Helps for Translators). New York: UBS, 2001. For this and other handbooks for translators see here .