After the starting room, head towards the exit of the ceremonial hall but don't enter it, then turn and find an opening in the wall with a few Cannonballs.
In the Chamber of Cosmos, between a pillar and the first staircase, there is floor that you can jump on. After doing so, stick to the right or left walls and move along to get the Super Health. If you try to get it by moving through the middle, you will be teleported back to the staircase (use this to leave the secret area after collecting the Super Health).
After the narrow bridge, before the second staircase, head left of it to collect some secret sniper bullets.
In the room accessed using the elevator, visit one of its corners, in the middle of them should be mouse-sized holes. Shoot them with any weapon to summon "deadly midgets" (extremely small Sirian Werebulls).
Before exiting the Chamber of Cosmos, visit the lamp on the right side of the ramp you slid from and spot a bouncer pad. Use it to access a secret area with some ammo, but immediately use the teleported located there after picking up the ammo as a Major Bio-mechanoid will spawn.
When you exit the palace and are outside, look to your left and you will see a humongous pillar with a warrior with glowing eyes carved onto it. Shoot a rocket at it to reveal a secret teleport.
In the courtyard with the third tablet, in the wall opposite of the entrance behind a statue is a darker section on the wall. Blast it to reveal an Invulnerability power-up.
In the courtyard following from secret #7, there is a health pill in a corner before entering the building and exiting the yard. Pick it up to spawn a "Mighty Gizmo" (a giant Marsh Hopper that will spawn several extremely smaller ones upon death).
After revisiting the first yard, go to the left of the entrance of the Tower of Babel to find a secret Invulnerability power-up.
After collecting all tablets, go to the door that leads to the yard with the first tablet again for a secret "round 2".
(HD-only) After entering the Tower of Babel, go behind the ramp-slide, behind the last pillar and look up. Shoot a rocket at the platform with the cannonball ammo to bring it down.
From #11, shoot the wall behind the ammo with any weapon to make it push the cannonballs to you, or else you will be teleported and unable to pick it up.
At secret #6, you can destroy all the miniature palm trees in the teleport to spawn a Super Health, and destroy the miniature version of Ugh-Zan III to spawn an armor (only works in the classic version). Blowing up the miniature version of Sam (with rockets, grenades or cannonballs) will kill the player.
In the secret round 2, there is a Serious Pack, Super Heavy Armor and Super Health at every yard. There is also a Serious Damage in the third yard, and a Serious Damage and Invulnerability before the fourth yard (in the building) in the hall to the right.