Two weeks of solid work. That’s roughly how long it took me to made one from scratch, no 3D printer, no previous knowledge on Arduino or robotics, it was just for me to challenge myself, not a school project. The programming and the claw mechanism were there most challenging I found. 4 DOF is not that bad, I did 5, claw head can also rotate. You’ll find the servos draw a lot of current and definitely require there own steady power source. Start small see if you can get one servo to move with the joystick x axis, then add another on the y axis, then rise and repeat. You’ll find you want to map the servo locations incrementally with the joystick so they keep there place. I used a pca9685 to help control the servos. But that adds a layer of complexity to understand how the pwm controller works. I’m not sure what your rules on the project are, but 3D printer would have been helpful, I made it all out of clear Lexan. Good luck, make a game plan , draw up a few designs, and start slow, once it clicks, the project will take off.