Trap it like a normal trap to argy or griffin. Be ready to try it more than once because it can snatch your from mount. Once trapped,

Ready your Bowgun turret with chain bolas ammo, use normal bolas through holes of the gate way trap to pin it down then lower it's hp. I recommend to use magnifying glass while its pinned down to know the hp left. Wait for it to free itself. Then shoot it with chain bolas. Feed it with raw prime meat. It's taming percentage (not quality) will go down fast as its hunger, wait for it to free again then shoot it again with chain bolas and feed it. Feeding interval is like in seconds.

More Tropeognathus Taming & KO Tips