A+ time: 7.50
Simply jump on the dissolving blocks to make them disappear, and jump through the hole you've created while avoiding the saws. To do this faster, when you are sliding down the bottom wall you can wall-jump while holding right to go right through the hole you've made. Hold left doing this on the top.
View a video walkthrough here.
Walls is the dark world counterpart to The Levee. In it, the bottom of both layers are completely covered in saws; on the bottom layer the walls are on each side of the pit, with one dissolving block in the middle; on the top the two walls are hanging from the ceiling, and are more in the middle than the bottom ones. There is a bandage on this level, on the ceiling between the two top walls.
A+ time: 11.00
Bandage: Yes (Not shown in picture)
Tip: hold sprint key for this whole level. Dissolve the first wall, then jump all the way over the pit, hold right while wall-jumping to get past the second wall. Slide up the far right wall and wall jump to the first dissolving wall and then jump back, dissolving two blocks (and not the very bottom one). Jump back to the hole you've made off the safe spot in front of the pit, hitting yourself against the top block and sliding down to the bottom block, quickly jumping off that block on to the second wall; then jump back to the very top of the first wall to get the bandage, and jump back, slide down and jump off the bottom block you didn't destroy to Bandage Girl.
Captain Viridian can do this level with no chance of failure by flipping and walking across the top wall for the whole level, but he requires 90 bandages to unlock.
View a video walkthrough with bandage here.