Here is a guide to unlocking every part in armored core 6. The rest of the combat logs and unlockable parts are impossible to miss. Make sure to look below for timestamps for chapters
and part unlocks!

0:00 - intro
0:15 - c1 destroy the transport helicopters
0:51 - c1 attack the dam complex
02:44 - c1 operation wall climber
03:17 c1 retrieve combat logs
03:53 - c1 prisoner rescue
04:45 - c2 infiltrate grid 086 Head (HC-3000 Wrecker) Bipedal Legs (2C-3000 Wrecker) Core (CC-3000 Wrecker) Arms (AC-3000 Wrecker)
07:52 - c2 stop the secret data breach
08:38 - c2 ocean crossing
09:17 - c3 steal the survey data
09:42 - c3 attack the refueling base
10:44 - c3 eliminate V7
12:02 - c3 tunnel sabotage Plasma Rifle (IA-C01W1: NEBULA)
12:36 - c3 survey the uninhabited floating city Generator (IA-C01G: AORTA)
13:32 - c3 eliminate the enforcement squads
14:06 - c3 attack the old spaceport
15:18 - c3 eliminate "honest" brute Booster (BC-0600 12345) Flamethrower (WB-0000 BAD COOK) Chainsaw (WB-0010 DOUBLE TROUBLE)
17:00 - c4 underground exploration - depth 1 Bipedal Legs (IA-C01L: EPHEMERA)
17:30 - c4 underground exploration - depth 2 Booster (IA-C01B: GILLS) Arms (IA-C01A: EPHEMERA)
18:47 - c4 underground exploration - depth 3 Core (IA-C01C: EPHEMERA) FCS (IA-C01F: OCELLUS)
19:43 - c4 unknown territory survey Head (IA-C01H: EPHEMERA)
20:13 - c4 reach the coral convergence Light Wave Blade (IA-C01W2: MOONLIGHT)
21:47 - c4 reach the coral convergence (alt) Light Wave Cannon (IA-C01W3: AURORA)
22:08 - c5 intercept the corporate forces
22:31 - c5 eliminate "cinder" Carle
23:10 - c5 MIA
24:43 - c5 regain control of Xylem IB-C03W3: NGI 006 Coral Missile Launcher IB-C03W4: NGI 028 Coral Shield