The training facility is 2e, 2s, enter from Tleilax AP.
Inside find a hidden door to enter the secret area. Find a sardaukar assassin hiding here and offer to help him.
Find two guards with halves of a key, kill them and take the key halves to the assassin. Now find two vials to store the samples. The vials are in hidden rooms, one is in the western training room and one in the eastern room.
Next head south and kill the Tleilaxu Master and pick up the note he drops. Unlock the door and enter.
Kill the shadow dancer (read the note first). Get the samples from the freezer, put them in the vials and give them to the assassin.