You don't have to pick the Line Gun like I did at the Primary Weapon screen since you have an opportunity to get that weapon early on in the Chapter (7:25), but I choose it anyways to have it readily available on the left arrow of the directional pad.
If you're quick, you can use the Flamethrower to rid of Swarmers. Unlike in Dead Space 1, Swarmers hardly do any damage, even on the Impossible difficulty mode.
The third Pulse Rifle Weapon Upgrade can be found in the vent in the room with the Line Gun. You should be able to clearly see it if you look up, but you'll need to shoot out the vent before you can use Kinesis to grab it. (7:29)
I recommend taking the route I show in the Zero-G Therapy room. Otherwise, you'll having to deal with potentially annoying Flyer enemies. They're not that hard to deal with when using the right weapons, but I much prefer easily dispatching Leapers with the Line Gun instead.
This video ends just before exiting the Zero-G Therapy room.
This video begins just before exiting the Zero-G Therapy room.
The fourth and final Plasma Cutter Weapon Upgrade can be found on a shelf on the right just past the Zero-G Therapy room. (0:07) If you miss it while walking by, you can use your short Free-Look opportunity to grab it.
The first Line Gun Weapon Upgrade can be found when Nate looks at the ship's hull in space from the breached room. (1:04)
The first Arc Welder Weapon Upgrade can be found on the left side of the Morgue. You get a brief chance to get it just after dropping out of the vent (4:37), but you also get two Free-Look opportunities to grab it and other items during breaks from the fighting.
The fourth and final Rivet Gun Weapon Upgrade can be found in the Emergency Room with Perry (the doctor that Nicole has a conversation with). You get your first brief chance to grab it when stepping out of the elevator (8:05), but you also have a few more short opportunities to grab it later on.
This video ends during a fight with Necromorphs in the Emergency Room.