You can also become an experienced medicine cat, and go on your own accord! I'd refrain from killing cats until the end, because you might need them for another acheivement.
It depends which clan you are in, and if you or your mate is the female (I think). If your mate is female, the kits should be in your mate's clan. The kits will be in a nursery.
Does anyone know how to find the she-ghost? I keep going when the moon is completely dark, but it wont work! If someone could help me out, that would be awesome!
Once you have an apprentice, talk to them to train. Go up to the brown she-cat in Fireclan (I forgot her name, but she is usually laying down. She is Plumclaw's aunt.) and click on her. She asks if you want to hunt, and you say yes. Then she explains how to hunt!