The Maor Veshemesh teaches us how to destroy Amalek; through Ahavas Yisroel. He proves it from the encounter with Amalek. תִּמְחֶה אֶת זֵכֶר עֲמָלֵק can be interpreted to mean: "erase זֵכֶר from עֲמָלֵק", meaning, take away זֵכֶר, which has the numerical value of 227, and subtract it from עֲמָלֵק, which has the numerical value of 240, and you get 13. Now, 13 is the numerical value of אהבה and אחד. When we are like "one" and have love for each other, then we can destroy Amalek. When there is "love" between 2 Jews we have אהבה twice, which equals 26, the numerical value of Yud-Kei-Vav-Kei – the Name of Hashem which represents Rachamim.
At the end of Parshas Beshalach, we have the story of Amalek attacking Klal Yisroel. It says: וְהָיָה כַּאֲשֶׁר יָרִים משֶׁה יָדו וְגָבַר יִשְׂרָאֵל וְכַאֲשֶׁר יָנִיחַ יָדו וְגָבַר עֲמָלֵק- "And when Moshe raised up his hands, Israel was victorious, and when he lowered his hands, Amalek was victorious." The Mishna (Rosh Hashona Chapter 3) explains this means: כל זמן שהיו ישראל מסתכלין כלפי מעלה ומכוונין את ליבם לאביהם שבשמיים היו מתגברין – "all the time that Israel Upwards and concentrated their hearts to their Father in Heaven they were victorious." Why does it need to say מסתכלין כלפי מעלה "that they looked upwards" and ומכוונין את ליבם לאביהם שבשמיים - "they concentrated their hearts to their Father in Heaven"? When it says Moshe Rabbeinu raised his hands, it means he raise his "koach", which was his great humbleness and love for every Jew. (The Arizal (I think) explains that the value of the word יד, hand, is 14. Two hands would then be 28, the value of the word כח, strength.) So, the saw the nation saw this and wanted to emulate it. When it says מסתכלין כלפי מעלה it means that they looked at the מעלות, "the good points", of their fellow Jews, and then they were able to direct their hearts to Hashem.
By looking at the "Ma'alos", the good points, of Klal Yisroel, we have the "Ahava" and the "Echad" necessary to destroy Amalek.