Okay. I have an alchemist who is taking a prestige class after level 5. (Specifically Sleepless Detective, but that's not important.)
I want Fast Bombs, if possible. The requirements for Fast Bombs says "An alchemist must be at least 8th level before selecting this discovery." This is, I assume, Class Level 8, not Character Level 8? Which is to say, when I get to A5/SD3, I can't buy the Extra Discovery feat and snag that.
So, assuming that's the case, what are my options? Is there any workaround for this short of taking the other three levels of Alchemist?
You are correct that it is referring to 8 alchemist levels being required to take the fast bombs discovery. I highly doubt that there is any work around to getting class features. If there were ways to get class features early then every monk would take 1 level of Druid, utilize these "ways" to get three "effective levels" in order to get Wildshape then take "Shaping Focus" to count four non-druid levels as druid levels for Wildshape thus resulting in 5th level Monks which can Wildshape like 8th level druids but with flurry and lots of other monkish things to boost their combat abilities. There are some archetypes that give certain abilities a level or two earlier - for example the weapon master fighters gets weapon training at 3rd level instead of 5th. I'm not sure if such a thing exists for the fast bombs alchemist discovery - you'd have to look into it, but I doubt it.
tl;dr Some archetypes grant class features early, but other than that, there is no way to get class features early.
Is there, then, any other way of making a non-iterative attack iterative? Item/feat/combo/whatever?
Well crap.
Closest you're going to get to fast bomb without fast bomb is getting a bag of fuse grenades and being a magus with Spell Combat and Fireball.