The story
From heel (“rear part of the foot, where it joins the leg”) + turn; sense 2 (“act of turning around abruptly”) is derived from turn heel or turn on one’s heel. Sense 4 ("A situation in which a wrestler previously identified as a hero changes to being considered a villain") is a pun on the word heel, which also means “a headlining wrestler whose ring persona embodies villainous or reprehensible traits”.
Etymology from Wiktionary, CC BY-SA 4.0.