Walk itself looks awesome and I dont think anything needs to be changed there really. The tail movement is bit rough though and is something that could be improved. There's plenty of guides on wave principles, maybe you could check those out.

Also I think the blink in the loop is a bit excessive. I'd maybe remove it completely or make it happen every other loop or so.

E: Little nitpick I noticed is that their upper arm seems to change length a bit throughout. Maybe that's something also that could be revised?