A student was animating a spider for a videogame, I gave him some suggestions and when I tried doing one of my own I realized the challenge and approached it the best I could.
Just like animating quadrupeds having the back legs do the contacts when the front the passing, I thought about it as "moving the fingers" playing a piano, so I made some circle guides for each leg offseting the pose of each leg. First I animated 4 frames, then I did the inbetweens and realized I could pull apart the legs further for clarity changing some of the poses and also offsetting the frames for each leag by one.
For the front view, it was all about clarity. If its not clear where the legs are, it's chaos. I used a reference to know where to put some the legs at the sides, but I used the same method I used for the side view.
The abdomen, and the head were animated with motion tween.
This is the spider sprite I found quite useful when animating the front view: http://rmrk.net/index.php?topic=17953.25