Voltage issues?

A couple of times within the past couple of weeks I’ve had my battery almost go out on me. I figured it was because I was leaving the car on the battery switch but then a few times this week. I actually had to have it boasted because it drained completely after that I had a plug in volt meter in the car plug in and noticed that the total volts was only about 13-13.5 ish volts while driving but when I let off the gas the volts jump up to 15-15.4 volts I spoke with a mechanic and he said it was the battery that’s pooched but I just want a second opinion on it.