Shadow Warrior 2

I found the easiest way to get any elemental kill achievements was to use a melee weapon with an elemental upgrade on it. The Bladez of Zaibatsu are dual swords that were unlocked in the second story mission, 'My Hero' as the reward for a side mission. Once you finish 'My Hero' you should have a decent amount of upgrades in your inventory, and hopefully, you will have an elemental upgrade. If not, the ninja shop may have some for sale. Put the upgrade on the Bladez and head into the next mission. Once you get the achievement related to your first upgrade, swap it out for another one.

You can also find upgrades that add bonus elemental damage, and ones that reduce enemies' resistance to elemental damage. These will make the achievements go much faster.

As far as I could tell, you did not need to actually kill the enemy with fire, only set them on fire. However, firearms do not seem to set enemies on fire as much as melee weapons. If you are running around trying to get the secrets while doing missions, this should be done within 1-2 missions.