Mortal Shell - All Weapons and Upgrade Materials Guide

I would suggest finding all the shells and weapons as you enter the Fallgrim Tower and the beginning of the game. This way you will get them all right at the start and you can choose whatever you see fit for the rest of the game. It's also easier to stick with one shell and weapon and to upgrade just those. This video will show you all the locations and even the boss fights to get the weapons, so be cure to check the description for timestamps to easily skip parts you maybe don't need.

6:03 - Hammer and Chisel Weapon - Defeat boss at the beginning of the Seat of Infinity area
8:15 - Boss fight
11:56 - Smoldering Mace Weapon - Defeat boss at the beginning of the Shrine of Ash area
14:50 - Boss fight
18:18 - Martyr's Blade Weapon - Defeat boss at the beginning of the Crypt of the Martyrs area
20:16 - Boss fight

---Fallgrim---
0:04 - Quenching Acid x2 (You can buy 2 per playthrough at Vlas's Shop for 2500 Tar each)
0:32 - Quenching Acid
1:41 - Quenching Acid (Inside the locked chest just right from the Fallgrim Tower lower floor door - need to raise the fog so you can get loot from the locked chests - you can do this after beating boss in other areas than Fallgrim)
2:03 - Mechanical Spike Weapon Upgrade (for Hallowed Sword)
2:35 - Molten Spike Weapon Upgrade (for Hallowed Sword - need to raise the fog so you can get loot from the locked chests - you can do this after beating boss in other areas than Fallgrim)
4:08 - Forbidden Offering (Buy from Corrupted monk for 3000 Tar - Shop left of the entrance to Seat of Infinity)
6:01 - Tools for Ballistazooka (Buy from Vlas for 8000 Tar and develop this at the Workbench)

---Crypt of Martyrs---
6:31 - Purified Winterglass Weapon Upgrade (for Martyr’s Blade)
7:03 - Quenching Acid
7:44 - Solemn Offering
7:58 - Radiant Winterglass Weapon Upgrade (for Martyr’s Blade)
9:13 - Quenching Acid

---Seat of Infinity---
11:05 - Quenching Acid (From the first torch in the middle of the first area; when you are facing towards the north stairs - take the east path)
12:47 - Perfumed Censer Weapon Upgrade (for Hammer and Chisel)
13:15 - Solemn Offering (starting point is from the first torch in the middle of the first area)
14:17 - Quenching Acid (from the 4th torch you will have to go upstairs and reach 2 teleports behind you on top; go inside the right one and then down on the platforms)
17:47 - Quenching Acid (same levels as where the teleporters are, just north towards the platforms)
18:49 - Foul Censer Weapon Upgrade (for Hammer and Chisel)

---Shrine of Ash---
19:27 - Foundry Stone Weapon Upgrade (for Smoldering Mace)
19:58 - Quenching Acid
20:49 - Solemn Offering (start from the previous Acid)
21:25 - Quenching Acid (start from the previous Offering)
21:42 - Awakened Stone Weapon Upgrade (for Smoldering Mace)