I'd check what the airline mean by "sports equipment". Many consider it awkward stuff like surf boards, golf clubs and bicycles.
Archery gear is usually just stuff in a big case. Whether you use a hard or a soft case pad it out with clothing, waterproofs, bubble wrap and foam.
Put your arrows in a tube not in the foam slots in the case lid (if this applied to how you normally transport them). I put foam in the bottom and top of the tube and put half points up/half points down and roll in bubble wrap so they're not flapping about in the tube.
For a compound bow you can use pipe lagging foam tubes to protect the limbs - the small guage will fit split limbs nicely and some of that fairly solid foam that you get in computer boxes can be use to protect the cams from end impact so it goes to the limbs instead - if you have it in a soft bag.
Just some tips I've picked up from others who had travelling experience.
I don't lock my bags I use plastic ties, but you need to remember to put something you can cut them off with into an unsecured pocket of your hold bag
