What I did was use my Ichthyornis to Hunt fishes and bring the dead bodies for me.
Change his settings to "Hunt and retrieve", put him on your shoulder then you go swim. While you are swimming aim at The fish you want and double tap F (on PC). Ichthyornis will fly, kill the fish and bring the body to you.
Then you take the body to Hesperornis and feed it. Once you get used to it it's very fast and easy. I recommend following Hesp from behind so you dont need to adjust your aim all the time.
Place a ramp on the outside of each of the walls & a ladder on the inside of each.
Speed is everything. If you have or can acquire an Ichthyornis first your tame will be forever more wonderful... later on that.
Place your trap just on the shore where you have seen Hesperornis running around. (It's a flightless bird). Find them at the edge of a swamp or around a secluded small body of water.
Antagonize a Hesperonis to make it follow you & walk to your trap. If you run, you'll probably disinterest him/her (preferably her).
Once in the trap s/he will stay put. Use the nearest ladder to get out. Now run to the water to gather fish. Kill but don't harvest. You'll see the E:Drag appear. Press "E" to drag fish to the trap. When you jump in you will lose your fish so be prepared to grab it again. ("E" to drag). Don't let her/him feed on it. You will see the Yellow "E: To Feed Fish". Press "E". Rinse; repeat until s/he tames out. Press "E" to change her settings first and foremost. "Behavior"- change
ATTACK Your... to "Passive", "__ only conscious, and "Low" on following-you'll thank me later. Now, press "E" to put her/him on your shoulder. SUCCESS!
Note 1: If you get and learn to use an Ichthyornis, it will catch fish for you and turn it into "Prime Fish" that waits for you to gather it and feed it to your Hesperonis. This is a much quicker and more effective Tame.
Note 2: Any fish will do, but Prime will do better, quicker, and better. If you cannot get Ichthyornis, you can make a fish trap from foundations placed in the water with a gate at the end. Two auto-gates work better, but cost more. Argo Salmon and lead them into the trap. This is very tedious compared to getting an Ichthy, which will always be useful.
How to get an Ichthyornis... Make sure you have more than one tranq weapon. Crossbows work well because they are faster than Longneck rifles. Use tranq arrows (Crossbow) or tranq darts (Rifle). Shock tranq darts are best because you won't need many and they will not kill your target (unless you spaz and pellet the poor bird). You can tame underwater if you must, but try to down it over land if possible. You have more than one weapon because your target will steal your weapons. :O This bird is worth your frustration, believe me. Not short… sorry.
The most frustrating thing about taming these guys is not only do they take a lot of fish but the same button to feed them is the same button to drop the fish(i don’t know if it’s different in pc or ps4)and it’s constantly swinging around your face making it annoying because you’re constantly dropping it. Either make it so the controls to feed them are different then dropping it or make ur so it’s not constantly in ur face.
Tame to this kill fish and drag there body to it and once tamed if you feed them more dead fish corpses it will build up and lay a golden egg which is used as a buff to certain dinos or oil or a player buff
Tried to tame one earlier (you gotta drag them fish. Don even do their own hunting like! Lazy birds) kept dropping the fish trying to feed them taming bar ended up going down when I was on 25.7% I gave up beestrd birds