The 1st weapon case can be found in the flooded area in the console room
The 2nd and 3rd weapon cases can be found on the obervation deck:
One will be dropped when you kill the Draghignazzo
The other can be found on the bench in the corner
The 4th weapon case can be found in the solarium at the back area
The 5th weapon case can be found at the bridge once you kill the Scarmiglione
The 6th weapon case can be found at the very last room on the side deck
The 7th, 8th, 9th and 10th cases will be obtained at the deck once you killed both normans
Congratulations. A full run will give you a total of 10 weapon cases and 6 illegal parts

Here´s an example of a full run:
Credit @Diamond Girls

You can have a rather quick run and still obtain 9 / 10 weapon cases. Here´s the order I reccomend:

1. Pick up the case in the flooded area

2. Obtain both cases at the observation deck

3. Head to the solarium. Get the case there

4. Then get the case at the bridge

5. Last step: Kill both normans at the deck. You will be rewarded with the last four weapon cases

Done. WIth a bit of practise you can finish within 20 minutes while still getting 9 weapon cases. Pretty succesful for farming weapons.

Example:
Credit @Diamond Girls