Simple predicate = the main verb (or verb phrase) without helpers like “might have been.” But watch out for helping verbs! In “She has been running for an hour,” the simple predicate is has been running (the whole verb phrase). If you just pick “running,” you miss the nuance. Nuance is fancy, but it’s also important.
And if you ever get stuck, just remember: Find the action, and you’ve found the treasure. The simple predicate is the treasure at the end of the grammar rainbow.