Shadow Warrior 3: Definitive Edition

This one is a little bit more tricky this time around as you have no weapons that can deal fire damage. However, I've found if you Chi Blast the explosive barrels at tougher enemies they won't die but will catch on fire. This doesn't work on the weaker enemies as they die instantly though.
Happy hunting.

If you spend the upgrade points in your Katana and upgrade it to level 3 you can then use a charged attack to do elemental damage. The game doesn't seem to explain this unless I just missed it. So once you collect enough grey orbs, (it will take 7 to upgrade the katana to level 3) you can do the charged attack. What I did was replay the first level, Way to Makoto. When you get to the first arena you will have 3 weak enemies spawn immediately. Just charge the attack and most importantly DO NOT hit them. It seems hitting them with the katana doesn't count for setting them on fire. What you need to do is swing and miss to the side or such like and the splash damage for the elemental attack will set them on fire. Before the fight ends, pause and reload checkpoint to repeat the process.

The only thing is I couldn't work out was how to do fire and how to to electrical damage. Sometimes the charged attack would do fire and sometimes electrical. Perhaps someone can clarify? Either way it won't take long once you have the sword leveled properly.

I upgraded the Outlaw to level 3 and unlocked this achievement on level 5. I had maxed out the sword first so once I unlocked this it didn't take long. I used it primarily until I ran out of ammo and eventually unlocked it.

According to the upgrade:

"Heats up bullets fired in quick succession, that set enemies ablaze."

There are many way to complete this achievement.

1. Use explosive barrels on enemies to set them on fire (enemies that die instantly don't count).

2. Upgrade your revolver to level 3. After that continuous shooting make it spit fire so that you can set enemies on fire with it. It counts.

3. Upgrade your Katana. It will throw fireball after holding down buttons (you can check details of the Katana update in game) to set enemies on fire.

4. There is exploding enemy later in the game (they just run at you while screaming), If you shoot them while they are near some big enemy, there is chance the bigger enemies will catch fire. But this is something to bank on, it might happen, it might not.

I got this achievement at: 03:33:15 - "Set the world on fire" Achievement
(mostly with explosive barrels and revolver)

I made a 100% complete guide for all achievements and challenge.
(All timestamps are in YouTube comment)

Not long after fighting your first Oni Hanma you will enter an arena with multiple of them as well as smaller enemies, if you stand at the lower level there are 2 explosive barrels which when shot near an Oni Hamna will set them on fire. You can easily reload the checkpoint to get this achievement quickly.