Before one can defeat a drake, wyrm and wyvern, one must find them.
There is a drake at "Devilfire Grove" from the beginning of the game.
However, unless one visits Bitterblack Isle's Rotunda of Dread, and chances to face a wyrm or wyvern there, the other two are not available until after defeating "The Dragon" who stole your Arisen's heart.
After "The Dragon" has been defeated, there is a wyrm at "the watergod's altar" and a wyvern at the top of bluemoon tower (where one fights Salomet to obtain the wyrmking's ring).
They may randomly appear elsewhere, and in certain levels of the post-dragon Everfall, but those are the easiest to reach.
Happy gaming!
