You should not start threads on the same topic, in 2 different sections of this forum.
Looking around youtube at some of the videos on 9g servo walkers, I see they probably aren't using controlled servo-speeds, just whamming the servos over to their target positions. That's probably ok, given the leg design.
Even with what appears to be "extra" torque servos, you'll likely still have a weight-vs-torque issue, so you cannot pile on too much stuff. However, the way they've designed those hip joints [ie, rotating on a vertical-axis], most of the force is held by the servo mechanical joints, and not by the servo torque itself, so you'll probably get away with it, as long as you go with the 2-DOF legs, and not try to implement 3-DOF legs, as mentioned in the other thread.
The original photo appears to show them using an Arduino ProMini, and that will probably be ok for totally controlling this thing. You can use the Rduino Servo library.
As I have it, a 1S Lipo battery only provides 3.7V, and that's probably not enough for the servos, which typically specify 4.8V minimum. So, you'll probably want to go with 4 AA or AAA cells in series [the AAs may be too heavy], and get the 3.3V version of the ProMini or whichever controller you end up using. You can buy ProMini knockoffs for about $3 on ebay.
Also, in general, it's easier to build a Hexapod as the first walker, rather than a Quad, as 6 legs are more stable and you have 50% more torque, and the gait is trivial. Just stay with 2-DOF legs for a starter.