For this achievement, you must find half of the game's secret passages.
There are a total of 18 hidden rooms in the game. Every level except levels 10 and 20 have a secret room. If you are not sure if the level has a secret room, or if you have found the room in that level, just look for the treasure chest icon in the level select screen. Each level with a treasure chest on the level select screen has a secret room. If the chests opens when you select that stage, it is informing you that you already discovered that stage's secret.
Below is a short description of where to find the hidden room in each stage. They are typically pretty easy to spot, as there is a distinct change of texture around the wall where the secret passage lies (it will be solid black, as opposed to the surrounding texture normally indicating a wall.
1.) There will be a short line of coins leading into a wall. Follow the coins into the wall.
2.) Just before the retracting spike trap, to the left.
3.) There will be a line of coins leading into the wall. Requires double jump.
4.) After a short cutscene about 'undead creatures', in room with chains, dash into the righthand wall.
5.) In the upper left corner. Climb chain to reach. Best to wait until the boss is dead.
6.) Next to the one totem that is just sitting on the ground, to the right of it.
7.) During the hanging chains section, to the right of the chains.
8.) Near the end, below one of the totems on the left (when it becomes transparent).
9.) In large water area, make your way to the far left.
10.) No secret passage here.
11.) This is definitely the hardest passage to find. There will be a line of coins leading into the lava at one point. Make a leap of faith into the lava to find the hidden room.
12.) There will be some breakable platforms that you must jump up to reach the room.
13.) At the beginning, go to the right. Use bombs to reach.
14.) At the bottom of the cave area, to the left.
15.) Upper left corner. Perform double jump off of the chain. Wait until the boss is dead.
16.) Very beginning. Blast blocks to the left.
17.) During the second chain section, near the end of the stage, the passage is on the right.
18.) First half of level, during chain section (very hard to miss).
19.) Bottom of chain, to the right.
20.) No secret passage in this stage.