HereForTheBeer: Thanks for the suggestion of the Fireforce perk. Sure enough, that made it downright simple to unlock this weapon last night, not to mention that it is very helpful on level 6.
The weapon itself.... I don't like it. Probably works better when combined with the (I forget the name) no self-damage perk. Otherwise, I was finding myself being locked into a corner by the results of my own weapon.
TheBitterness: Fireforce is the perk I play with damn near all the time, it's simply too useful for me to consider much of anything else -though I do welcome the diversity and challenge that others offer. With that said, I've had the fortune to snag upwards of at least 18 and at most 20 badges in one run (not stage) before, however I've not found but 3 secrets in one stage. Whether this owes more to my particular style of play, luck in badge drops to help aid discovering secrets or both is beyond me, but that badge run told me that no small amount of luck is going to be necessary if I'm going to have the stuff necessary to really go hunting.
For my part, I'll be leaving this for an attempt at 'Endless Mode'.
Right now I've been playing around with different combinations of weaponry and mods as I come across them. (Currently 2/12 with 2 of those 12 being to the Maw and 1 of them being the Gumball Machine and I taking each other out at the same time). I've found that when it comes to weaponry I really am not a fan of the 'bubble gun', though I respect the damage it can do, and when it comes to mods I have no use for 'Spread', 'Seek' and 'Mine'. Mines are too tragic when encountering the boss pair that look like iron Pac-Men, Spread makes it remarkably difficult to hit the Gumball Machine's light (especially with my favourite gun, Egon's Pride) and Seek just does not work when it comes to the Gumball Machine. If there was the option to completely jettison a mod at any point in time during play I'd be set but, as it stands, those mods I see, say 'no sir, good day' and keep on my way.
Fireforce + Egon's Pride/Consolation Gun/Pizza Launcher is just my favourite way to play. Save for my last run with the Mine mod, I've found between 2 and 5 Extra Jump badges and that really is a life saver. Relying on luck, as it were, to help with finding the badges seems to me to be the way to go when trying to both complete the run and unlock the gun at the same time.
For finding secrets, look everywhere. Some of them are hidden behind passable (for lack of a better term) walls; these are fairly easy to find by simply shooting at the walls and looking for the spots where your ammo doesn't collide. Others are 'hidden in plain sight', as it were, being cleverly disguised with the graphic textures so you may not notice that there is a little alcove just around that corner right over there. Hopefully this isn't a spoiler but note that, with Fireforce, there is some lava swimming you can do that will lead you to at least four secrets (one of them an "uber" secret). There other hint is to look up, and do so from different angles. In the Foundry in particular, at least one room has three secrets that are easy to get to but aren't obvious to find unless you take some time to wander around a bit. You can get to them without Fireforce but make sure you have full health before doing so.
You're right, though, some of them you will not normally be able to get to without certain badges or specials, like the ramp or, umm, I think it's called the togatrooper - the wings that let you fly for ten seconds or so. Endless Mode sorta solves that, and the cake level can also take care of that problem once in a blue moon.
For perks, I really like Luck. This one increases the chances of badges appearing, so you'll have more opportunities to gain multiple jumps and increased jump height. Be careful taking too many jump height badges. They're great for finding secrets but you can get yourself in trouble fairly easily with three or four height boosts. Pretty fun, though.
Speaking of which, having that ability to jump high and long makes the Sanctum boss, and also The Maw, pretty easy to defeat. Just keep yourself in the air as much as possible - especially for the Sanctum boss - and they'll go down much faster since you'll have to worry less about survival and can concentrate on putting shots on target.
For Endless mode, you have a pretty cool weapon to unlock: slower rate-of-fire but very high damage from the get-go. Note that you do not need to go to The Maw in Endless mode - it'll wrap around back to the foyer if you choose to take the normal teleporter after the Sanctum boss.
Oh yeah... spoiler coming up but I think it has been posted in another thread:
There are at least two guns that you can use to boost your jump height, using their recoil once you're in the air for a pseudo-flying ability. Not super-easy to control, but it does work. This can help you access some of those secret areas located above you.