Fight fire with fire? What an excellent idea. You should fight everything with fire.

Firebug is an excellent archetype for offensive purposes, so long as you don't do a lot of fighting in libraries or other extremely flammable environments. Depending on the circumstances, a Firebug might end up burning a lot more than intended. For those interested in this archetype, that's probably half the point.

Firebug Wield fire.
caret-right Fireproof Ignore and snuff fires.
caret-right Hellfire Empowered Burning condition.
caret-right Molotov Toss flammable oil.
caret-right Pyromania Burn things, restore Energy.
caret-right Wildfire Make it spread.

Firebug

Offense plus-circleBurninate: As an action, you may inflict the Burning condition on any subject or flammable environmental feature within throwing range (0-10 meters).

minus-circleWeaponized: This ability suffers failure chances from cover, concealment, and size differences between yourself and your target just like weapon attacks do.

minus-circleSupplies: Roll a trigger die when inflicting the Burning condition this way. If the result is 1-3, then doing so costs 1 Supplies. You cannot use this ability if you have no Supplies remaining.
Offense plus-circleFirebrand: You know how to enhance your weapons with flame. Whenever you make any weapon attack and the trigger die is 10+, you inflict the Burning condition to your target in addition to all of that attack's normal effects (damage, conditions, etc).

minus-circleMonoelemental: Your weapon attacks can only inflict a single elemental condition on a 10+ at a time. If you have levels in multiple elemental archetypes, you pick which condition your 10+ trigger die attacks inflict each time.
Condition Explanation
burning-embers Burning minus-circle When rolling to remove condition at the end of the round, lose 1 Flesh if result is 1-4 and lose nothing if result is 5-8. Rolling to remove as an action during the round does not cause damage regardless of trigger die result.

minus-circle All spaces within 1 meter are fully lit, all within 2 meters are dim light (or fully lit if they were already dim light).

plus-circle This condition is automatically removed by getting wet or entering an airless environment.

plus-circle This condition is automatically spread at the beginning of each turn to any adjacent creature that is grabbing or being grabbed by a creature that already has it.

Fireproof

Protection plus-circleFlame Sheath: You no longer take any damage from the Burning condition. If you have the Burning condition and don't want it, you can remove it from yourself as a free action at any time during your turn.
Utility plus-circleSnuff Out: As an action, you can put out all fires (including both environmental fires and the Burning condition on any creatures) in a 1-meter space within throwing range (0-10 meters) of your location.

plus-circleKill the Lights: Any Light items in the target space (either held by a creature or unattended) are extinguished and must be re-lit to regain their benefits. Illuminator lights (from the Outfitter archetype's Illuminator ability) are immune to this effect.
caret-right Alternative plus-circleMass Quench: You can put out all fires within 2 meters of the target space instead of only the target space.

minus-circleSupplies: Snuffing massive fires in this manner costs 1 Supplies.

Hellfire

Offense plus-circleNapalm: Fires you start (both environmental and via inflicting the Burning condition) cannot be quenched by water or by transport to an airless environment. They'll even burn in space.

plus-circleCharnelhouse: When creatures attempt to recover from Burning conditions that you created, they lose Flesh on a result of 1-6 instead of 1-4.

plus-circleBrilliant: Fires you set are brighter than normal. All spaces within 5 meters of the target become well-lit, and all spaces out to 10 meters increase light level by one step (darkness → dim light → well-lit).

Molotov

Utility plus-circleFirebomb: You can toss a lit flask of something burny to any point in throwing range (0-10 meters) as an action. The target space and all adjacent spaces catch on fire and become difficult terrain (requiring two meters of movement speed for every one traveled). Any creature in the area when you throw the Molotov or that subsequently passes through any space covered by your burning puddle immediately gains the Burning condition.

plus-circleBurnout: Burning oil puddles exhaust their fuel supply and go out on their own at the end of the current exploration turn unless there was something else flammable nearby to spread to.

minus-circleTool Cost: Roll a trigger die when throwing a molotov. If the result is a 1-3, then doing so costs 1 Supplies. You cannot use this ability if you have no Supplies.
caret-right Alternative plus-circleOil: You can choose to throw non-lit oil instead of a molotov. This makes the target spaces difficult terrain as usual but does not catch them on fire. If any source of fire touches an oil puddle, the entire area instantly bursts into flame as per a normal Molotov.

Pyromania

Protection plus-circleHeh Heh Heh: Burning things gives you a deep, satisfying thrill. Every time you set something on fire or apply the Burning condition to a creature, you regain 1 point of lost Energy (up to a maximum equal to your Flesh).

Wildfire

Offense plus-circleTo Destroy All You've Done: Fire tends to spread much more quickly when you're around. At the beginning of your turn, you can set fire to one space or inflict the Burning condition on one creature of your choice within 20 meters as a free action.

minus-circleSpark Seed: You cannot set anything on fire with Wildife unless it is located within 2 meters of another source of flame (burning environmental space or creature with the Burning condition).
caret-right Alternative plus-circleConflagration: You can spread fire up to three times at the beginning of your turn as a free action instead of only once.

minus-circleThrow Some Gas: Spreading fire rapidly in this manner costs 1 Supplies.