It's Mt. Pico de Loro (which is Spanish for Parrot's Beak). I'm actually standing at the peak when I took that picture. That steep monolith in the picture is called, ironically, the Parrot's Beak as well. Sorry if it seemed that's the mountain, I guess we're even in terms of misleading titles and pictures lol. You would need to climb down from the peak if you want to climb ... the beak. It's about 15-20 meters tall, and it's 100% rock. I'm not a wall climber so I had a very difficult time scaling it, but I eventually made it to the top. There wasn't that much room at its top though. I'd say about less than 2 meters wide. It was scarier than climbing up and down the whole mountain, but reaching the top of it gives a more solid sense of accomplishment.
And, you're right, going down posed more of a challenge! There were points where I didn't know how the hell I got up from because it almost looked impossible to go down.