Talk to Bard Rukal (Dion). He says in order to practice high-level elemental magic, you must fully understand the temperaments of the four elements. The test of Magus examines how much you know about this.
Talk to Parina (Gludin). Parina sends you to the Wasteland to talk to Wiseman Casian. He can be found southwest of the south Ant Nest entrance (south of the "a" in "Wasteland" on your ingame map)
Singing Flower Phantasms are on the largest island in Fellmere Lake.
Singing Flower Nightmares are west and south of the waterfall northwest of Ivory Tower.
Singing Flower Darklings are north of a small pond that is south of Giran. Follow the path south of Giran and turn west right before you get to the bridge.
Return to Bard Rukal. He sends you to find patrons for each of the four elements.
The Water Undine is west of Fellmere Lake, directly west of the SF Phantasms.
Hunt Toad Lords and Swamp Stakatos in Cruma Swamp, near the tower, for 20 Dazzling Drops. Return to the Water Undine.
The Fire Salamander is in the Ruins of Despair (south of the word "of" in your ingame map).
Hunt Ghost Fires in the pit that surrounds the Ivory Tower for 5 Flame Crystals. Return to the Fire Salamander.
The Wind Sylph is east of the path you take to reach the Wastelands from Gludin, right where the grass turns to sand.
Hunt Harpies in the area just north of Giran Castle. After you get the Feathers you need, travel to Death Pass and kill Wyrms to get the 10 Wyrm Bones. Head north up Death Pass, but instead of crossing the bridge into Oren territory, turn east. Follow the river until you find Windsuses. Collect 10 Windsus Manes and return to the Wind Sylph.
The Earth Snake is in The Ruins of Agony/Sorrow, north of the space between "The" and "Ruins" on your ingame map.
Hunt Enchanted Monster Eyes, Enchanted Iron Golems and Enchanted Stone Golems in the pit that surrounds the Ivory Tower. Get 10 quest items from each, then return to the Earth Snake.
Talk to Bard Rukal and he gives you the Mark of Magus.