How Sheldon concluded that the Amalek tribe and their cows should be killed?

Because the Amelekites attacked the Israelites on their way out of the desert when they were led by Moses, as the following text (with Biblical reference) shows:

God then pronounces the Amalekites' doom, commanding Moses: "Write this on a scroll as something to be remembered and make sure that Joshua hears it, because I will completely blot out the memory of Amalek from under heaven." (Exodus 17:14) This event occurs near the beginning of the Exodus, before the incident of the Golden Calf, and we do not hear of the Amalekites again until nearly 40 years later. As the Israelites prepare to enter the Promised Land, Moses reminds them that the Amalekites are not to be forgiven:

Remember what the Amalekites did to you along the way when you came out of Egypt. When you were weary and worn out, they met you on your journey and cut off all who were lagging behind; they had no fear of God. When the Lord your God gives you rest from all the enemies around you in the land he is giving you to possess as an inheritance, you shall blot out the memory of Amalek from under heaven. Do not forget! (Deuteronomy 25:17-19)

And the following:

It would be the kings Saul and ultimately David, however, who finally fulfilled—or nearly fulfilled—the doom pronounced earlier by Moses against the Amalekites. Saul "fought valiantly and defeated the Amalekites, delivering Israel from the hands of those who had plundered them." (1 Samuel 14:48) After this, God commands Saul to exterminate the Amalekites entirely:

I will punish the Amalekites for what they did to Israel when they waylaid them as they came up from Egypt. Now go, attack the Amalekites and totally destroy everything that belongs to them. Do not spare them; put to death men and women, children and infants, cattle and sheep, camels and donkeys. (1 Samuel 15:2-3)