Ramchal-Kinas Hashem Tzvakos-Amalek
עֲמָלֵק (Amalek) represents the טֻמְּאָה (Tumah-ritual impurity) that was placed into חַוָּה (Chava-Eve) by the נָחָשׁ (Nachash-Serpent) . This טֻמְּאָה (Tumah-ritual impurity) is also represented by the עָרְלָה (Orla-foreskin) which is why the גְּמָרָא (Gemara-Talmud) describes the חֵטְא (Chet-sin) of אָדָם הָרִאשׁוֹן (Adam HaRishon-Adam) as מוֹשֵׁךְ בְּעָרְלָתוֹ, that he enlarged his עָרְלָה (Orla-foreskin). When אַבְרָהָם אָבִינוּ (Abraham) reached the age of 99 he was informed that it was time to remove that טֻמְּאָה (Tumah-ritual impurity) and he would then be complete. This would constitute a removal of any connection to the סִטְרָא אַחְרָא (Sitra Achra-other side). In מִצְרַים (Mitzrayim-Egypt), which was known as the עֶרְוַת הָאָרֶץ, the corruption of the land, the Jews neglected to do בְּרִית מִילָה (cirumcision) which allowed the טֻמְּאָה (Tumah-ritual impurity) to encroach upon them again. This situation was reversed when they left מִצְרַים (Egypt) and had a בְּרִית (circumcision) on the way out.
To take this one step further, you need to understand that עֵשָו (Esau) represents the left side of טֻמְּאָה (גְּבוּרָה) where the טֻמְּאָה of the נָחָשׁ is greatest. He was the spiritual heir of קַיִן who was also from the צַד שְׂמֹאל (left side). Whereas עֵשָו merely possessed this טֻמְּאָה, his grandson עֲמָלֵק epitomized it. The good of קַיִן had gone to יִתְרוֹ whereas the רַע had gone to עֲמָלֵק. The descendants of יִתְרוֹ originally dwelled amongst the עַמָלֵיקִם, and it was once they separated from עֲמָלֵק, leaving עֲמָלֵק with only the רַע, that the destruction of עֲמָלֵק was possible.
The תּוֹרָה was given to כְּלַל יִשְׂרָאֵל in order to rid them of the טֻמְּאָה of the נָחָשׁ. This is why the concept of the power of תּוֹרָה is encapsulated in the פָּסוּק of זֹאת הַתּוֹרָה אָדָם כִּי יָמוּת בָּאֹהֶל (This is the law of a man who dies in a tent), on which חז"ל comment that תּוֹרָה will only remain by someone who kills himself over it. But why in a tent? The tent is an allusion to the tent of יַעֵל who was from the family of יִתְרוֹ. It was they who separated from the ultimate טֻמְּאָה, that of עֲמָלֵק. But the same goes for each of us, we must separate from the טֻמְּאָה of the נָחָשׁ that is within each of ourselves through the power of תּוֹרָה study.
עֵשָו by marrying into the family of יִשְׁמָעֵאל incorporated within his descendants also the right side of טֻמְּאָה, the side of חֶסֶד. It is for this reason the תּוֹרָה says וְהַיָּדַיִם יְדֵי עֵשָו, the hands are the hands of עֵשָו. The use of the plural indicates that both hands were now his. However, this is only if אֵין הַקּוֹל קוֹל יַעֲקֹב, if the voice isn't the voice of יַעֲקֹב. As long as his voice is being heard through the study of תּוֹרָה, עֵשָו has no hands.
On the way out of מְצָרִים the nation was attacked by עֲמָלֵק in רְפִידִים. The גְּמָרָא explains that this indicates שֶׁרָפוּ יְדֵיהֶם, that their hands were weakened in תּוֹרָה study. . That left עֲמָלֵק strong and the weak hands were pointing sideways, no longer cleaning the tent. עֲמָלֵק attacked כְּלַל יִשְׂרָאֵל and cut off their organs and tossed them to the sky. This was to indicate their rejection of the concept or removing the טֻמְּאָה through a בְּרִית. Still, they only managed to harm those who had been kicked out of the protective clouds due to their improper behavior. The סִטְרָא אַחְרָא only gets that which is already his.
מֹשֶׁה had to go the next morning and raise his hands. His hands to oppose the two hands of עשו. He went to רֹאשׁ הַגִּבְעָה, literally the top of the hill. But רֹאשׁ is occasionally used to mean the opening. Wherever there is an opening, the סִטְרָא אַחְרָא has an opportunity to take hold. It was there that מֹשֶׁה needed to be in order to protect כְּלַל יִשְׂרָאֵל. He stood there with the מַטֶּה, his staff which had been the נָחָשׁ and reverted to being the מַטֶּה to show the subordination of the טֻמְּאָה to the קְדֻשָּׁה.