Two Worlds

You will need to first appropriately level up any school of magic so that you can use 5th chamber spells. (I personally put 15 skill points into the Fire school) When hovering over the magic schools on the skills menu (where you'd level up) a small message will tell you what chamber spells you are capable of casting for each school. Once it says you can cast chamber 5 spells in whichever school you've chosen, you're half-way there!

The second part is to actually find a 5th chamber magic spell card. You may or may not already have one. (Had I done this more efficiently, I'd have first found a 5th chamber spell, then leveled up that school) These can be obtained as random loot drops or purchased from Society vendors. (I personally had to purchase a chamber 5 spell for the Fire School, but I had received chamber 5 spells as loot for the Earth and Necromancy schools.)

When the 2 above criteria are met, it's time to equip the spell. On your magic page, make sure you move the chamber 5 spell into one of the magic card slots on the left side of the screen. (add any boosters if you wish) Rather quickly, press the D-pad button in whichever direction you wish to "hotkey" the spell to and confirm your choice with LT. (You won't be prompted to confirm and taking too long will have you changing the menu page, not setting your hotkey) When the hotkey is setup appropriately, it's time to find a victim. (more fun that way, but you can cast magic even without an enemy present)

Make sure the magic spell card you're trying to cast is shown in the upper left hand corner of the screen, below you're health bar. Change spells by using your D-pad and selecting the direction that we just hotkeyed your chamber 5 spell to. Cast your spell and the achievement should unlock.

To unlock this achievement, you have to scouer the game world for at least one 5th Circle magic spell card under any school of magic. Once obtained, make sure you have the neccesary mana to cast the spell. If not, go to any of the skill resetter mages in the game world and pay the nominal fee so you can pump the freed-up Param points into Willpower to boost your mana reserves.

Once the neccessary requirements are fullfilled, hotkey the 5th Circle spell and cast it to unlock this 10GS achievement.