The fact that there are only two Parts (as opposed to the usual three) for this Chapter implies that it's fairly short. It is, but Chapter 9 more than makes up for the short length of Chapter 8.
The fourth and final Flamethrower Weapon Upgrade is found right at the beginning of the Chapter. (0:17)
By the way, the scare with Eckhardt and the Slasher was one of the only ones that actually got me when I played through the game originally.
The rolling capabilities of the Force Gun's alternative fire (a timed grenade) is one of my favorite weapon capabilities in this game. It's very effective for knocking the legs off of Slashers and for ripping apart Leapers.
After entering Shuttle Bay 47, you can find the second Contact Beam Weapon Upgrade off in the distance but next to the shuttle. (6:22) Shortly thereafter, you can find the third Arc Welder Weapon Upgrade when looking inside of the shuttle. (6:45)
This video ends just after the big fight in Shuttle Bay 47 is done.
This video begins just after the big fight in Shuttle Bay 47 is done.
Off in the distance in the room with the four power cores is the second Ripper Weapon Upgrade. Your first opportunity to grab it comes after Weller says "There - the power cores..." (2:44)
I originally disliked the way the ending to this Chapter was panning out, but a twist happens and turns it into one of my favorite moments in the game.