What does the Torah mean when it writes that Bil'am saw Amalek?
Rashi: It means that he saw the punishment (the downfall) of Amalek.
Ramban, Rashbam and Targum Onkelos: It means that he actually saw Amalek from the vantage point where he was standing. 1
Why does Bil'am refer to Amalek as "Reishis Goyim"?
Rashi: Because they were the first to attack Yisrael 1 (after they became a nation).
Ramban: Because they were a leading power among the nations. 2
What did Bil'am mean when he concluded "ve'Achariso Adei Oveid"?
Rashi: He meant that ultimately, Yisrael will destroy Amalek. 1
Targum Onkelos: 'Ultimately, they will be destroyed forever'.
Targum Yonasan: 'Ultimately, in the days of Mashi'ach, they (Amalek) will join forces with the nations of the east to wage war against Yisrael, but all of them will be destroyed forever'.
Rashi: As the Torah writes in Devarim 25:19 "Timcheh Es Zeicher Amalek!" Rashi in Koheles (8:9): 'I saw and I took to heart ... how one person dominated another and overpowered him, and how ultimately, it turned out to his detriment: Amalek overpowered Yisrael, but in the end "ve'Achriso Adei Oveid" - and that is what happened to Nevuchadnetzar and to Sancheriv'.
Ramban: As the Torah writes in Sh'mos 17:14 - "Ki Machoh Emcheh es Zeicher Amalek!"