You are pretty much lapping the corners and as you stack the 4x4’s up drill down through each corner and every 18” the length of the timber and pin them together using either rebar and/or 8-12” 100d galvanized nails. Also, the treatment used for pressure treated lumber has changed (not all treated lumber is the same) make sure whoever you get to build it uses lumber that is treated for ground contact or marine use. This will prevent rot from water as well as where it touches the ground.
I built something similar a few years ago to hold my juvenile turtles, although I used 6x6’s, which I would recommend using instead of 4x4’s it will hold up much longer.