The only way to get lvl 11 and 12 crystals are by having them in your inventory while raiding a major boss monster such as Antharas, Valakas, Lilith, and Anakim. I'm sure one or two other mobs can do it as well, but otherwise, the only way to get them was the medal event, which will hopefully return in about a month.
According to Stratics, it can be done (on the boss on the Commander levels). Has na "Unconfirmed" status though.
Would be really great to get some official info on this.