Firstly, you need mutagen, and a lot of it for a high level. On my 5X taming servers, it was roughly 4% per feed.
To actually tame them, you need to do the following:
1) find the creature. They are always in space, and have the most probability of appearing at the top of the spawn zones in Space. Look around the asteroids at the North and South ends, that's where I tend to find them.
2) you need to take it down to below 10% of it's health, where it will start glowing blue. It's breath attack is annoying because it stuns you for 5 seconds, and it breathes on you like a person with Halitosis does on the bus.
3) once it's health is down, you need to get close and ride it like you would an equus. The mutagen should be in slot 0 because every time it does a "barrel roll", you should be feeding it.
I haven't found a way to not get bucked off 2-3 times, depending on the level, and if it aggros Astrodelphis, they can slow you down and allow it to get away and heal. It heals pretty fast, not as fast as a reaper though.
Using the creature... It's a Tek variant wyvern. It's breath attack doesn't seem to do damage, but it has a stun effect that let's you get a few free chomps. The longer you hold the breath action button, the more stamina you burn, so only hold it long enough to immobilise your victim
People never read non-violent incorrectly. It doesn’t mean it isn’t hostile, it means you don’t beat it into unconsciousness as it tries to run away because it knows you’re about to halfway murder it, non-violent in this case is a bull ride.