Triggering Awakenings is PURELY RNG. Upon using a skill in battle, it can absolutely at random trigger a passive effect you can put on it. Each one of these effects is 1 unique awakening, you needing each unique awakening on one singular skill.
This can only be done post-game, as the game locks you out of unlocking a certain 3-4 until you beat the final boss/get the ending, it seems. They are as follows;
Affinity
Blight
Chain
Criticality
Destruction
Elusiveness
Empower
Fate
Hasten
Limitless
Manifestation
Pierce
Quickness
Resolve
Restoration
Stun
Weaken
Wither
My recommendation for this is using someone other than Aisha throughout the post-game 101 floor dungeon, with the best Awaken Chance shadestone, and the best skill cooldown shadestone you can on their weapon, and use the same skill as often as you can. This is incredibly easy to unlock, it's just not doable until post-game and even then it'll take you a few hours of use, but luckily if you've used a Daemon throughout the game, to then use them in post game, it'll make it much easier as you've got the majority of these unlocked.
Once all of these are unlocked on ONE skill, you'll unlock the Omniscient trophy.