Photographing moving objects is tough with any camera. A couple of tips:
1. Lighting is extremely important. If you're outside during the day, your shots will be better. If you're shooting indoors in an arena, refer to #2
2. Keep the phone as still as possible. Rest it on a bench or something to take your action shots. If your subject is moving, your photo might be a bit soft, but if your subject and your camera are moving, you'll get a blur for sure.
3. Try recording a video and snapping pictures while recording. I find this makes capturing action in dim lighting a little bit easier. This way, you'll also have a 1080p video that you can snip a few frames out of if you want. Not ideal, but probably the best you'll get in poor shooting situations.