If you have a friend and an argentavis easily take these by picking up one which is not fleeing while your friend in a ghillie suit is a ways away. Fly over and hover low enough that they can pet them but not so low the hyaenodon touches the ground. Be sure the person on the ground is out of line of sight before you hover and then sneaks behind the hyaenodon to pet. They don't have to move between petting. If it spooks then drop it into an enclosure and move out of rendering distance. We were successful without ghillie suits but you have to be perfect at sneaking. Scaring them makes the time meter go down.
Normally you can't tame the pack leader, so just get a pteranodon or argy, pick it up and drop it in a large area (like a separate section of your base). When you take it away from the rest of the pack, it removes its 'pack leader' title, allowing you to tame the highest level hyena of that pack.
Despite it's appearance, the real life hyaenodon was nowhere near related to actual hyenas, but it actually belongs to a group of prehistoric mammals, all extinct, that are believed to be most closely related to pangolins, which aren't related to anteaters or armadillos, for your information.
I used a combat argy to follow them around till they got stuck on something. Tamed a 145 and 150 both times they just walked in place while I sat there and hit E every 30 secs. Don't leave the argy to close or they will continue to try and flee even while stuck.