Following this walkthrough you'll see every CG in the game with very little hassle.
First, set the CONFIG to these settings:
This will allow you to speed through the game using

(same button turns SKIP off). If you want to be less cautious, change that first setting in BASIC to the right. This will make it so the game will skip over everything and won't stop when a call comes in and such. Luckily, the game tends to Quick Save right before any calls come in anyway so you can quickly fix any mess ups. There is an important RINE message you have to read on 12/15 that the game tends to outright ignore when speeding through so you have to be aware. To that end, I've included pics of what the screen looks like when each text and call comes in so you know what to watch for! And, when viewing endings, make sure to watch all the way to the credits starting so you see any CGs.
To "ignore" a call, just don't even bring up your phone with

. You just continue on.
Chapter - Absolute Zero- No choices to make.
Chapter - Missing Link- No choices to make.
Chapter - Closed Epigraph** Save 01 **
12/15 (WED): After you receive a call from Amadeus, Okabe can turn off his phone. There's no real prompt to do this for the non-Japanese speaker, but just choose to do so by pressing

and selecting "OK" after the mandatory call.
Chapter - A Stray Sheep- No choices to make.
Chapter - The Orbital Eclipse** Save 02 **
01/02 (SAT): Ignore the call from Amadeus.
ENDING - Twin Automata** Load 02 **
01/02 (SAT): Answer the call from Amadeus by pressing

and then

.
Chapter - Anitomic Dual** Save 03 **
01/02 (SAT): Answer the call from 080X208X705 by pressing

and then

.
ENDING - Promised Rinascimento** Load 03 **
01/02 (SAT): Ignore the call from 080X208X705.
ENDING - Recursive Mother Goose** Load 01 **
12/15 (WED): After you receive a call from Amadeus, Okabe can turn off his phone. Choose not to or don't even bring your phone up.
12/15 (WED): During a chat with Fubuki and Kaede, Okabe will have a flash of his more cheery self from the Steins;Gate world line. (Only occurs if ENDING - Promised Rinascimento was already viewed)
A text will also come in. Read it by pressing

and selecting "RINE". You can back out using

.
Chapter - X-Day Protocol- No choices to make.
Chapter - Pandora’s Box** Save 04 **
01/23 (SAT): Answer the call from Amadeus by pressing

and then

.
ENDING - Gehenna’s Stigma** Load 04 **
01/23 (SAT): Ignore the call from Amadeus.
Chapter - Presage or Recognize- No choices to make.
ENDING - Vega or AltairENDING - Milky-way Crossing (Only occurs if ENDING - Promised Rinascimento was already viewed and the 12/15 RINE message was read)
Now go to the Main Title, select EXTRA, and then CG LIBRARY. This and all other CG-related achievements should unlock!