Alright, so here's the plan:

1. Have Elise the Enlightened copy Moonfire, Germination and Imprisoned Satyr.

2. Once you have Malygos in hand, drop both Imprisoned Satyrs

3. You got 2 turns to empty your hand of occasional minions (Thats why all of them are cheap in this deck except for Maly itself).

4. Imprisoned Satyrs go off, making Malygos 0 mana.

5. Drop the free Maly + 2 Germination on him (we're at +15 spell dmg for 8 mana)

6. Moonfire is now 16 damage x 2 = 32. Pew pew our opponent is dead! (Steps 4, 5, 6 are in one turn).

This is the win condition.

The rest of the deck has a quest shell, lots of good choose ones, removals and plenty of draw, so we can safely reach our goal :)

(Not 100% sure on the Wild Pyromancer and Ironbark..)

Edit: Removed Ironbark and Wild Pyromancer to replace them with Licensed Adventurer and Escaped Manasaber. Both these additions help complete the quest as early as possible.