your question was, can you get by with an ocean view in Miraflores for 1400 a month and the answer is yes. There are all sorts of rates in Miraflores, so you need to really pound the pavement to find the best deals. Having been through many apartment searches, I suggest a good approach is to combine your efforts, check all the websites, especially the Comercio on Sunday mornings, but also keep an eye out.
I have helped a couple friends find apartments and the way I found one of my apartments was getting a taxi and renting it for the hour (20 soles is a good rate, you might find a few soles less, a few soles more) and driving around because some apartments do not advertise with anything other than a sign in the window and I often find those to be less. Last time I was looking, I found a place not 2 blocks from the ocean, but no view, 3 bedroom for 580 a month, so bargains are still to be had in the area, though the place was in a very old building.
One thing said was helpful, find a temp place, maybe a hostal (they have them here that are not all dorms, but more like cheap motels that are basic and not too bad) and give yourself 2 or 3 weeks to really pound the pavement if you have the time.