Run backwards and sideways while changing direction a lot, you can't do that unless you're on your toes. Play tennis, soccer, or any other sport that requires sudden changes in direction. Tennis is good because nearly all movement is lateral. And of course, shadowboxing. Focus on movement.
Balance. Work on stance, footwork drills, not just skipping but hopping and getting a feel for the ground. Work on calves, hammys, glutes and lower back for support.
I would say skipping rope while mimicking the types of movement you do in a boxing ring has helped me a lot.
One way is catapult, both feet together then toe and heel as you resist, the elastic with the knees slightly bent. Needs consentration but a lovely number. Plus another one with rollerskates, will make your eyes water :good