I do not recommend simply screwing this assembly together. There are a variety of ways to attach the members such as glueing, glue and screw, metal angles with screws, specialty hardware etc. Before we can answer I suggest that you address a number of additional design considerations beforehand.
- Vertical framing support at the ladder: The top bunk left side must be supported at its corners. This means that frame must be attached to the wall or supported by a column extending to the floor. and the outer corner must also be supported all the way to the floor. Since the ladder stops short of the floor to allow the pull out bed to extend, it cannot carry the corner all the way down.
- Bed frame sides: These can be made of plywood which should be strong enough to carry the weight, but there will be a problem making connections to the end panels or columns. Beds often have special hardware to make that connection which also allows the bed to disassemble easily. There are other options which are less easily unconnected, but either way the plywood may require fasteners that extend through the sides with exposed fasteners which is something to consider.
- Wood Type: Whether you use plywood or solid wood for the bed frame sides, you will need a second piece of wood on the inside to support the bed slats. This added thickness will also serve to keep the sides lined up straight. The plywood especially will want to twist a bit near mid span when loaded with weight and the extra thickness from the slat shelf piece will help either wood type to resist twisting. The shelf piece should be glued to the sides.
- Side Guard Railings: What you currently show is problematic, especially if they are made of plywood. Consider that they will be leaned and pulled against as users get in and out of bed. Think of the connections at ends and corners as pivot points. The connection between the wood pieces must resist the forces and prevent the rail assembly from twisting and pulling apart. These connections will be challenging enough with solid wood, but much more difficult to handle with plywood.
- Attachment Details: I do not recommend attaching the side frames to the end plywood panels by simply screwing through the back of the end panels into the sides. The ability of the screws to hold-on to the plywood is probably inadequate over time and use. I definitely recommend some sort of metal connections such as angles or specialty bed frame hardware.
- Exposed Hardware: As currently conceived, there will be a need for a lot of exposed fasteners. You should consider the hardware and connector types, appearance and locations in refining your design.
While the design concept for your bed assembly is doable, it should be refined in much more detail before it is ready for the shop. Feel free to post your design, with changes, in a new question for additional responses. As you develop the design you are bound to have a number of detailed questions. You can add more questions to discuss these more focused design detail concerns as you progress.
