So I haven't finished the game and I haven't actually read through the thread, but it seems like some of the latest posts in this thread are talking about not being able to break the lime green/dark green/purple blocks, and I just managed to get how to do break those blocks myself, so I'll write this down:
For location names, I'll call the one you start with the Suburbs, the green dank area the Abandoned Sector, the yellow castle thing with a blue night-sky background the Laboratory, and then the Clocktower.
The lime green blocks can be broken after obtaining the small green crystal that boosts the attack power of the float-jump gem. The earliest you can get one is probably from the just-out-of-screen hidden item in one of the connectors between the Laboratory and Abandoned Sector (accessible by highjumping up from the hub). Hit the blocks with the small tornado the float-jump gem generates.
The dark green blocks can be broken after obtaining the 8-way dash attack skill: the second boss (rapier) will talk about wanting a Jade-Green Seed when talked to in the hub. You need the Water Spirit's Blessing (obtained from an alternate route through the Laboratory, one of two that involves a lot of water; it allows you to sink in water instead of float). You then head to the great bridge with endlessly respawning mermaid warriors, go right one screen, go down the great big watery pit in the middle of the room, and take the route to the right. Give the Jade-Green Seed to the second boss and she'll give you the dash attack skill.
The purple blocks can be broken by the light-dark fusion attack skill, which can be learned from the Pale-Dark Sword Art Book key item stored in a metal treasure chest in the Laboratory. It's the one in the room where you need to flip two switches (one from the left and one from the right) to access.
By the way, for getting to hard-to-reach platforms, aside from using the ghost's levitation subweapon (technically it's supposed to be more of a defensive/invulnerability subweapon), you can generally get everywhere between using double jump, high jump, superjump, the float-jump gem (wind spirit's gem), the 'pogo' move you get pretty much automatically after getting doublejump (down+jump after doublejumping), the 8-way dash, and the invincible slide-behind-the-enemy skill you get from the third boss (scythe). Sadly I've not played Castlevania games so I don't know what the move's actual name is supposed to be. At least until you get the aerial high jump.