The secret on the deathrun map called "Tropical Island" is:

When you are the ending, you can pick 3 kinds of endings, Bhop, Knife, and an ending where you watch the deaths die slowly in a glass cage.

But there is also another secret ending, which requires you to know the code, so here is the code in the following order:

Press the button below all the numbers, then fill in the following code in this order:

7251

The secret ending should now be available for you!

The next map would be called "Sonic", and if your on the fix; deathrun_sonic_fix, then you can go to the secret ending, now you would be thinking: "Don't I need to collect all the rings for the secret ending to open?"
The answer is a simple no, as there is a secret button in a secret passage, and I will be telling you how to enter this secret passage:

After you have passed Amy, with the swinging hammer she throws, you come at a part, where there is 3 traps, 1 auto trap, where the floor breaks if you stand on it or just break it by attacking it, and the traps that are controlled by the deaths, when you have passed those traps, you shouldn't jump of the ladder where you enter the next stage, where shadow is at, you climb the ladder, jump onto this thing right infront of you which is black, and face to the left, and crouch-jump over to the deaths when you're nearly about to fall off, you should now be in a secret passage with a sonic character in it called "tails", what you're going to do is touch the wall behind tails, and face tails his tail, now don't move your head, just go to the left, and then go upwards until something prevents you from doing so, look a bit to the ground, and press E all around it, when you've done that, there should be a portal-like thing in the wall at the ending, it's at the left wall, and should be easily found, go into it, and you are now in the secret ending., congratulations!

The next map is Iceworld or deathrun_iceworld_v4. There are 3 buttons to activate then a code at the end.
The first button is under the 2nd cold air vent on the left (3rd trap). To help find it there is a color change of the wall under it and press e all around there. The 2nd button is after the trap were it closes the doors and crushes you. After the trap there is a corner on the right as soon as you get out if the the trap. Crouch into the corner and look straight into and press e all around. The 3rd button is on the left side of the whale under water. Crouch into that corner and press e all around then continue to the end of the level.
At the end of the level there is 4 buttons with bells. You want to hit it in this order: 2431. Then walk through the door and watch death get blasted into space.

The next map is Goldfever or deathrun_goldfever. There are 4 signs with skulls and the first one is right before the first trap. The second sign is after the second trap, which is under ground.The 3rd sign is before the stairs when coming out of the underground.
The last sign is at the end, you will have 4 choices but if you hit the sign the secret reveals itself in the back. Blast the death with a cannon!