So make sure you have it trapped before you try to tame it because it will take off and fly rampant across the whole map and lead you on a wild goose chase, this happens when it is close to being knocked out. This happened to me twice, once it lead me to a giga then flew into its mouth then the second time across the map for 30 mins. Also make sure you use tranq darts because arrows will kill them.

More Snow Owl Taming & KO Tips