Scratch that... 13 mins
I think this may be about as fast as it gets.
Click till 240, recruit, unlock catapult, get catapult
Keep clicking, buying catapults when you can, until you need to recruit.
At about 8-9 catapult, unlock alchemy.
Buy Infused, Jeweled, Molten (at this point, clicks are semi pointless)
Fill up (not max out) on catapults, get Brittle, Resonant, Enriched.
Buy Tunnel, max out catapults, unlock Arrow, max out Arrow, max out Reload, buy Elven, a few Arrow Damage, buy out all Alchemy, keep buying Resonant and Enriched.
At this point Catapults will only have 1 or 2 left to max.
Alchemy should be cleared out.
Arrows will be down to damage only.
Start getting cannons, to just add a little at the end. (they dont do much, but its the only thing to really spend much money on, and shouldnt cost much to max out either)