Secret #1
Right at the beggining, turn back around and you should see a gong behind a door. Shoot it and turn around quickly: the picture will slide revealing the first secret. Get it quick since it's time-based.


Secret #2
In the area where you get the yellow key, you can walk on the small ledge besides the window where there are ninjas shooting at you:

Run on that ledge and jump towards the window across it. From there, jump into it to get the second secret (and the achievement "Singapore Live")


Secret #3
After using the yellow key, and entering the room, if you look to your right, you should see a trash bin and a darker colored wall up high. In order to reach it, shoot the trash bin with the SMG/Riot Gun until it's close enough for you to open the secret and jump inside it.


Secret #4
From the last secret, proceed down the conveyor belt, to the room where you drive the car with the silver key. Then, go around the other conveyor belt in the room. You'll arrive to a room which can be seen when going for the yellow key. There are some lockers in this room. Two columns should be slightly brighter. Open them to get the secret.


Secret #5
After the room with the Koi fish, go to the back of the room where there are several lockers. One of them will be brighter. Use it and you'll hear a door open. Quickly run towards the Pachinko Parlor, and a secret door will be open to the left of the entrance corridor of the Pachinko Parlor.


Secret #6
Inside the Pachinko Parlor, there is an ATM machine right beside the places' sign. Use it and look behind you. A pillar with ads will drop revealing the secret.

Secret #1
In the room with the Yellow Key, Zilla's picture can be opened to reveal a switch. Activate it and look behind you where a secret comparment opens.


Secret #2
In the same room as the last secret, there is a ventilation shaft. Break the shaft and walk inside the vent to its end, where the secret will count.


Secret #3
In the area besides the blue key door (also, where there is a window to the gold key door room), jump to the highest stack of crates (beside the Missile Launcher ammo). Face the Medkit lying at the top of the metal grid and jump to it. Look behind you to see a UZI and a Heat Seeker card. Jump to them to get the secret.


Secret #4
In the room with the Gold key door, the machinery to the leftmost of the door can be opened, revealing a secret.


Secret #5
When going to the Blue key door, look at the first stack of crates to the right of the door (only a part of the crates can be seen). Open the stack to reveal the secret.


Secret #6
As soon as you enter the room after using the Blue key, look at the machinery at the top of the room. Jump to it and open to reveal the secret.


Secret #7
Before attempting the secret, make sure you get the Repair Kit, located beside the Blue Key:

With the kit in hands, proceed to the main area with the broken forklift. Fix it and drive it beside the mounted cannon. You should see a Nuclear Warhead. Jump atop the forklift and then to the area with the warhead to get the secret.

Secret #1
After ringing the gong and getting inside the temple, across from the switch that rotates a compartment with Sticky Bombs is a sign "Master Leep's Throne". Look up and you should see a crack. Blow it and jump to the room at the top to get the secret.

Inside, there's a medkit to the left and, if you press the button beside the girl, the toilet reveals a Night Googles. Actually, you don't have to kill the girl: just jump on top of her to collect it! =)


Extra 1
Also, notice the switch at ground level that reveal some Sticky Bombs beside it when pressed. In fact, the entire pillar rotates so if you press the button and run to the secret, you'll get a Missile Launcher! - credit to @dennoace2 for pointing this one out


Secret #2
In the room where you get/use the Yellow key, there's a stack of crates with a picture of Master Leep and some girls at the top. Jump to it and open the portrait to reveal the secret.


Secret #3
After getting the Bronze key and diving thorugh the small canal to the outside area (with the Bronze key door), look back from where you emerged and you should notice that the top of the waterfall is an area. Jump inside it and dive to get the secret.


Secret #4
While inside the room of the previous secret, notice that there's a switch behind a turbine. Activate it (by shooting) and run back to the outside area, open the Bronze key doors and jump to the stack of crates to your right. At the top a compartment will be opened with the secret. Be quick since the door closes on a time basis.


Secret #5
In the room with the Shooting Statue and the strange green-moving liquid, shoot the gong to raise the step. Then, jump to the pillar with the aforementioned gong. Finally, jump to the ledge with the Night Googles. If you look across the ledge, you'll notice a switch. Shoot it and a secret area opens right beside you.



Secret #6
After you blow open the way to the canyons, there'll be a rabbit standing alone:

Follow it and see it perform a leap of faith:

Do the same and jump (moving close to the opposite wall to ensure you'll fall in the water). At the bottom, jump to land and there'll be an entrance nearby:

Enter it to get the secret (and see Chan's grave). Also, there are teleporters on each side of the grave. One takes you directly to Master Leep (providing a nice shortcut), and the other takes you to a hidden area (though not a secret) with a Full Kevlar Armor.


Secret #7
After surviving the crushing trap (by blowing the exposed mechanism), simply jump inside the blown-up mechanism to get the secret.


Secret #8
From the last secret, solve the block puzzle. Once finished, return to the crushing trap. A wall will have raised, revealing a ladder and some Sticky Bombs:

Climb the ladder: there's a Grenade Launcher to the right (you'll have to jump to get to it), and a Full Kevlar Armor to the left. The secret should count as you move towards the armor.

Secret #1
After opening the Bronze key door, and before entering the room with the Gold key, look to the right and you'll se a wooden piece - cracked. Explode it to reveal the secret. Once inside, activate the switch to disable the trap in the Gold key room. There's another explodable wall at the end of the secret to get inside the room.


Secret #2
After using the Gold key, navigate the village area until you reach a large open building with a garden inside and a big pillar in the middle with a picture. Jump into the picture to get the secret.


Secret #3
Once you reach the Ripper Valley, look at where the river ends. Dive at that point and swin to the other side to get the secret.

As a side note, follow this valley to the end to reach the Monty Python reference and the "Unordinary Rabbit" achievement.


Secret #4
Back to the Ripper Valley, climb the waterfall where several Rippers are. Notice the large boulder partially blocking the way in the river. Circle it and follow the river to the end where a small crevice to the left contains the secret.


Secret #5
Near the end of the level, in the place where you have to control the pillars to make your way, you can notice a small crevice from where you control the pillars:

You'll need to position the pillars in order to reach it, more or less like this:

Get to the second pillar and fall to the hole in the wall (be careful, as you'll inevitably take some damage from the fall), to get the secret. A teleporter will open to take you back to higher ground.