Prodeus

Easy to do on a level called "Memoriam" since it's short and the hardest difficult is not really that hard. Just make sure you have full ammo when entering the level. There is only one secret in the mission and that is to shoot at a lower platfrom from the edge of the arena. you can open the map and look where the lower platform is. Memoriam is the sixth mission from left path

NOTE: if you set your difficult to ultra hard at the start of the mission you need to restart the mission from the pause menu.
Easy to complete with

EDIT: players have confirmed this has to be done deathless!

Memoriam secret:

I earned this on my first try on the Memoriam level. Their are only 45 enemies in a wide open area and no enemies spawn until you hit the switch out in the middle end allowing you to max out your ammo. After hitting the switch you must quickly jump up to the armor on your left and up to the rock area beyond it, double jump is required. You can hide behind the rock pillar here and take your time, enemies will spawn slowly as you pick them off, although to get them to spawn you may have to walk out to your right along the memorial, quickly heading back behind the pillar as they spawn.

Besides the usual fireball throwing and flying enemies you'll need to watch out for a shotgunner who stays in the middle and the sniper who will appear above the starting area after the halfway point. The rest of the enemies including some shotgunners will pile up along the memorial beneath you and it's easiest to bounce grenades down there to wipe them out.

All enemies must be killed, you must not die, and only one secret is in this level, enemies also shoot much faster and take more damage on this difficulty. For the secret, stand out on the platform to the far right end of the starting area and look down to your left and the bright spot on the ledge far below. Shoot it a few times to open up rocket/grenade ammo near you on the left. If you need rocket/grenade ammo do this before you start the fight.

After trying and failing multiple times on level 10, I did it on level 1 "Sacrum". I did this after beating the campaign.
Set difficulty to "Ultra Hard". Make sure you have full ammo (play the trial levels to fill ammo on whichever gun you need ammo for). Go slow, and remember that you need all kills, all 5 secrets, and you cannot die. I used the pistol on single zombies, the auto shotgun or shredders on multiples or shotgun guys, the auto shotgun on the imps (if they were close, if they were far away I used the zoom shot on the chaos gun), and the rocket launcher on the flying fat things. Remember that there is a switch on a half wall about halfway through the level that you push to drop a wall revealing 2 shotgun guys. Also check your automap periodically to make sure you aren't leaving badguys behind, this level is quite linear.

This will also unlock

Here is the link to the collectable guide by ShadowEchelon91


And here is the part from THEIR GUIDE (I'm trying to give them full credit) that pertains to this level.
Sacrum
1/5 After you fall down into the area with the partially opened door and collect the nexus point, the next room has what looks like 3 beds or tables. The door next to them can be interacted with to reveal a secret.
2/5 At the red key elevator, climb on top and jump over the nearby glass wall.
3/5 Immediately after secret 2, head outside and jump on the rocks next to the left and then again into a small area with armor.
4/5 Right after collecting the Shredders, drop down and turn around. There is an intractable door here with a faint "interact" symbol on it. Open it to reveal a secret ore.
5/5 After collecting the red key, immediately go left to find a ramp. Follow to the end for secret.

Good luck!