I'm in the beginning of Artus Topside. After a cutsceen that Jan instructed me to save the prisoners immediately. I saw an AT-ST in a canyon area and shot at it but got killed immediately by it. I reloaded and ran straight to the office at the foot of the canyon. I killed the trooper and the officer in the office, grabbed a key and started the elevator, I rushed on the elevator, got on top and found a turret. I destroyed the AT-ST in the canyon with the turret, and swung it around to wipe out the troopers on the wall opposite to the platform where the prisoners were, but got a "Too many prisoners have died" messege seconds later.

The next time I arrived the turret, I used it to shoot the troopers on wall first, but died of the fire from the AT-ST in the canyon.

The next time again I shot the canyon AT-ST first, then turned around to concentrate on the troopers, but still couldn't save enough prisoners from the troopers on the all. It seens there is a time lag here! Weird! I was quick enough!

I'm afraid if I made too many prioners die in the Artus Detention Area when I released them. One thing I'm not afraid it no prisoners died in the warehouse at the end of the detention area level.

Please help!

You have to kill that first ATST.. otherwise it will kill you  
Once you got rid of it, use the turret for the troopers on the high ledge on the other side. Don't take too long with this, if you're finding it hard to aim, get out of the turret and use a gun instead.
DONT get too far from the turret though, because soon another ATST will come out from this garage thing underneath the troopers and you'll need the turret to get rid of it asap.

It took me a few tries, but you'll eventually get a good sense of timing on how long it takes to kill the troopers and ATST's.

7

I never even got that far in the game.  lol

Nope.  Never got past the 2nd mission.