Agree with everything Doug mentioned already. The key for packing a horn in the case as checked luggage is to prevent it from moving AT ALL inside the case. The inflatable beach ball is great. It doesn't have to be fully inflated, just enough so that when in the case it's cushioning the bell from the inside of the case and preventing any movement in that direction. You can also use bubble wrap and clothes to help pad the horn inside the hard case. If you want to check how secure it is after packing, close up the case (with all the padding/beach ball inside) and give it a bit of a shake. You'll be able to feel if the horn is shifting around at all.
An extra layer is using a luggage strap around the exterior of the case (I like to loop it through the top case handle) to help keep the case securely closed, in the (hopefully unlikely) event that the latches fail or are broken off in transit.
Also, make sure there's nothing else inside the case (mouthpiece, valve oil, etc) that can potentially get loose and knock around the inside of the case, or get placed back loosely in the event TSA opens up the case for inspection. Speaking of that, I would take photos of the instrument inside the case once you're done packing, clearly showing exactly how you padded and packed it. This way, if it's damaged in transit due to TSA taking it out and not repacking it correctly, you'll have some more evidence on your side when filing a claim. Fortunately I've never had my horn damaged any of the times I've had it as checked luggage (now I use a gig bag on Southwest), but taking photos is useful just in case.
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)