Brawl is a dual-layered disc. It takes a little more out of the Wii to read and will almost certainly be the first thing it has trouble reading if/when the laser begins to die. To put things into perspective, it loads everything as fast or faster than Melee if run on the Wii from a USB flash drive instead of a disc--this is something I have to do because my Wii's laser died. Zelda transforms into Sheik the instant that the first animation with her moving her arms is over. Even the loading screen before the opening video just after booting the game is essentially non-existent, appearing only for a split second presumably because it's programmed to appear at least for one frame even if it's not needed.
Achievements wouldn't account for a significant amount of data. They'd be flags, much like done/not done objectives in, say, an RPG, and a series of yeses and nos. The single most taxing thing on games has always been the graphics, and in 3D graphics, texture files take up the most space by a long shot. Guess what game has an excessive number of redundant textures?
In addition to two files per character, one containing their attack data and one containing all animations, character-specific effects and sometimes weapons, every character's every color has two files. Both contain the model, a low-poly copy of the model used as their shadow, and their textures. One is larger and one smaller but the only difference is apparently the file's format. The larger only ever seems to be loaded when playing against computers in Classic, when your own character reaches Master Hand, or if the character swaps their model out for another (Zelda, Red, Samus, Wario, Bowser; Bowser is the only one in the entire game who seems to use the larger file under all circumstances) and I have no idea why they couldn't have just had one each. Mr. Game & Watch is a unique case, possessing only one file for the playable colors, no textures whatsoever, and numbers that define what color each one's body and outline should be.
Almost everything on any menu in the game pops up in at least two places. There's an entirely separate, independent set of the character select screen portraits that's only used for the fight results screen. The stage select and My Music menus have more or less the same sets of textures too.
Subspace Emissary enemies don't have their own files independent from the levels. This means that if you can find a Goomba in a level and you open that level's file, you're going to find its model, textures, animations, attacks and stats in there too. If you really wanted to you could change these and have Goombas look and behave entirely differently from one level to another, simply changing files and never adding any new ones. Plenty of levels also use the same textures, so many of the same textures are present in multiple levels' files.
Trophies also use their own models and textures whether the depicted thing is in the game already or not, but this does make more sense and most of them are frugal about it, being immovable meshes in the poses they are, without bones or alternate face meshes (not that either would make the files significantly larger).
I've been around the block and back with Brawl's guts. They're kinda nasty.