To get to Punta Arena from the old town, we had to take a cab which you drop us next to the New Hospital of Bocagrande, next to a beach where small boats leave to the island. Right when we entered the parking lot with the yellow cab, a ton of locals gathered around the car, trying to take us to their boat, with of course the cheapest deals. It was really annoying cause some of them were pulling me. I got a bit a angry and told them to let me decide where I wanted to go. Luckily, Marina tool the lead and found us a good deal: for a round trip and a pick up at the beach at 4pm we've paid no more than 30 000 pesos which is around 8 euros.
The internet websites were right about one thing: the beach was not crowded at all, but for the rest, we were pretty disappointed: the prices were way more expensive than on Playa Blanca (which is suppose to be the main beach in Cartagena). We were not able to swim because of all the boats and the water was smelling petrol. I took a swim to get fresh. Once I got out I was smelling gasoline so bad, and the smell stayed for a week, despite my cleaning efforts.
Despite the smell, we have a good time over there, friends, sun, beers and musics, what else do you need ?
Even though I wouldn't recommend to go this beach if you have spare days in Cartagena. You should definitely go to the Rosario Islands which are way better and with less pollution. Apparently the water is cristal clear and for those who want to do some snorkeling.