Inverse kinematics is the bane of walking robot builders. That fiddly trigonometry is hard to get right, and then you also have to take care of the correct movement profile and generating the servo signals over time to execute the motion. Why not use legs that have a tiny little microcontroller built into them, which takes care of all that stuff for you?
Just attach them to your robot, connect them over I2C, and send commands telling them to what position they should move. The leg will take care of it, without you having to worry about it.
But there is more. Hardwired movement is not good enough for your robot. Give it the sense of proprioception! By attaching additional wires inside the servo, you can turn it into an encoder and a force sensor. This way your robot will always know what positions its legs are in, and what forces are acting on them. Why is this useful? Well, you can make it respond to pushes and shoves, you can detect when it's about to walk off a table, you can can make it stand up after being flipped over, etc.