Here is a photo of a job we did about 3 years ago. This is dry-stacked with 6 oz non-woven geotextile backing.
The first thing that I noticed in your photos was that the stone was vertically stacked. This is very unstable, especially on a sandy substrate. Notice the slope that we used. This allows for a portion of the weight of the wall to be borne by the soil and results in a very stable wall. You seem to have a good variety of rock sizes. Utilize the largest (widest) rock for your base. This will help distribute the weight over a larger area. Gradually move to smaller rock as you build up in height.
Use of the geotextile is very important. In the area of the wall that is underwater, it will prevent the unavoidable loss (erosion) of soil through the voids and gaps between the submerged rock.
"Everybody is ignorant, only on different subjects." - Will Rogers