Which sentence is correct? One: I will be taking a shower at nine o'clock. Two: I will take a shower at nine o'clock.
They are both correct. See explanation.
Both sentences are correct, but there is a little difference in meaning.
The first sentence says that in a moment in the future a person will be in the middle of an action, while the second says only about the action and the time when the action begins (nothing about action's duration).