Tip1. Monsters that can level crystals
The following list is listing the highest stage a monster can take a crystal to. (so if a monster is listed by stage 9, you can take any crystal up to stage 9 on this monster, but no further), monsters that isn't labelled with (Not confirmed), has been confirmed and tested for C4 for their crystal stage.

Stage 1
Stage 2 Garden of Eva: Light Worm, Nos, Blade Stakato, Blade Stakato Worker, Blade Stakato Warrior.
Timak Outpost: Timak OrcOr, Timak c Warrior, Timak Orc Soldier, Timak Orc Archer, Timark Orc Troop Archer, Timak Orc Troop Warrior.
Stage 3 Devils Isle*: Unpleasent Humming, Light Bringer
The Forest of Mirrors: Forrest of Mirror Ghost(L46), Forrest of Mirror Ghost(L47)
Garden of Eva: Blade Stakato Drone, Water Giant, Queen Undine Lads.
Timak Outpost: Timak Orc Overlord, Timak Orc Shaman, Timak Orc Troop Leader, Timak Orc Troop Shaman
Stage 4 Devils Isle*: Death Flyer, Fiend Archer, Musveren
The Forest of Mirrors: Mirror, Forrest of Mirror Ghost (L48)
Garden of Eva; Evas Seeker, Theeder Piker, Theeder Mages, Garden Guard
Stage 5 Devils Isle*: Zakens Royal Guard, Kaim Vanul, Pirate Zombie Captain
The Forest of Mirrors: Harit Lizardman, Harit Lizardman Grunt, Harit Lizardman Archer
Garden of Eva: Doll Masters, Garden Guard Leader.
Stage 6 Devils Isle*: Doll Blader, Sairon, Sairons Doll, Sairons Puppet , Vale Master
Giants Cave: Halingka, Yintzu
Stage 7 Giants Cave: Paliote, Hamrut
Stage 8 Giants Cave: Kranrot
Stage 9 Devastated Castle: Doom Servant (Not confirmed)
Stage 10 Devastated Castle: Doom Guard(Not confirmed), Doom Archers(Not confirmed), Doom Knights(Not confirmed)
Tower of Insolence: Erin Edunce(Not confirmed), Platinum Tribe Series(Not confirmed), Angel Series(Not confirmed).
Antharas Lair: Malruk Knight(Not confirmed), Malruk Beserker(Not confirmed), Malruk Lord(Not confirmed), Limal Karinness(Not confirmed), Karik(Not confirmed), Pytans(Not confirmed), Pytan Knight(Not confirmed)
Stage 11 Boss/Raid Monsters: Anakim, Baium, Lilith, Antharas, Valakas, Zaken, Ember (unconfirmed), Anakazel(68) (Unconfirmed)
Stage 12 Boss/Raid Monsters: Anakim, Baium, Lilith, Antharas, Valakas, Zaken, Ember (unconfirmed), Anakazel(68) (Unconfirmed)
Stage 13 Boss/Raid Monsters: Antharas, Valakas, Ember, Anakazel(78)

* The Greater versions of monsters that level crystals (like Greater Musveren, Zakens Elite Guard, Kaim Vanul Ladd, Zombie Captains Spiritual Body, Crimson Doll Blader and Crimson Vale Master) are not able to level crystals.

Tip2. Leveling a crystal to stage 11 and 12

For creating stage 11 and 12 crystals, there are the following changes:

You can only level a crystal to stage 11 and 12 on Anakim, Baium, Lilith, Antharas, Valakas, Zaken, Anakazel(68) (unconfirmed), or Ember (unconfirmed).
An entire party can level up crystals to stage 11 or 12 at the same time. You do not need to drain or do anything else. You only have to make sure that you only have one crystal in your inventory (level 10 or 11) and that someone in your party gets last hit. So you can level up to 9 crystals each time you kill one of these bosses.
You cannot fail at leveling a crystal to stage 11 or 12 as long as your party got last hit on the boss, unless its a lesser boss like Anakazel(68) or Ember. Note: Reflect Damage can get last hit.
A crystal can never break when attempting to level.

Tip3. Leveling a crystal to stage 13.

For creating stage 13 crystals, there are the following changes:

You can only level a crystal to stage 13 on Antharas, Valakas, Ember or Anakazel(78),
An entire party can level up crystals to stage 13 at the same time. You do not need to drain or do anything else. You only have to make sure you only have 1 crystal in your inventory (stage 12) and that someone in your party gets last hit.
You cannot fail leveling a crystal to stage 13 on Antharas and Valakas. Ember and Anakazel(78) are not 100% success rate and each individual member of the party has a failure rate on leveling.
A crystal can never break when attempting to level.