First what you will need to do is get the sword to drop or… buy it from the broker, but that can be a little expensive.
The Fire Sword drops from Dried Gnarls　and Mottled Basilisks. Here is a picture with their general location.

The first part of this quest chain is obtained at level 25 from “Garperos, Daeva of Flame”. He is located at “Sataloca’s Grave” on the right side of the path standing in the middle of a huge jaw bone.

After that you will have to kill some Flame Spirits and collect their Flame Essence x3.

When you finish with that, just go back and talk to Garperos to get your new sword.

If you are interested in a detailed class guide for your character with tons of information, I highly recommend the Killer Guides Class Guides. They make leveling up so you can get swords like these, easier and more fun. Check them out here: Killer Guides Class Guides.