Voltage drop on Solar Cell MPPT
The characteristic of a loaded solar cell is just about a constant current source until you hit the a maximum voltage and then it drops off fairly quickly. The trick with MPPT is to get to the top voltage end of that constant current region.

I believe that you are probably taking just a little too much current. Your algorithm should be seeking a maximum for V*I for the solar cell.  

Your current sensing is at the battery end of the circuit it should be looking at the current from the solar cell. I also do not see where you are sensing the solar cell voltage.

Your switching transistor is connected back to front as per your diagram, the body diode will be conducting giving you a straight transfer from input to output with a bit of voltage drop. Allowing for current for the LEDs this explains your input to output characteristic.  

You need much bigger smoothing capacitors on the input and output in addition to the ones you show depends on your frequency but >=220uF.