To drastically reduce the completion time, you’ll want to press and hold 
to skip through the entire thing until there is a choice to make or something to do (the game will stop skipping automatically).
Let’s start by choosing the highlighted option in the below image of the game’s main menu to begin the story:
Now, as soon as the game starts be sure to press and hold to skip all the dialogues until you get to a pinkish screen with white text, gaining the following achievements in the process:
旅の始まりリリィが旅の目的地である紫影の塔を目にした。
Easy, huh? When was the last time you got a bunch of achievements for holding a button? Anyway... Press 
and you should now be at the below screen which has a bookshelf with The Washington Post on the top shelf.
Highlight the newspaper using 
and select it by pressing , then press a second time and you should be at another pinkish screen, press once again and you should now see the below screen with 3 pieces of paper on the screen:
Highlight the top piece of paper using and select it by pressing . After the pinkish screen (press to continue) you can read the piece of paper (if you can read Japanese, of course).
Every time you select a piece of paper, there will be 3 options (parts of the text) that you can highlight using 
or 
to choose from, using .
This time, press or 3 times to highlight the bottom option and select it with :
Now skip the pinkish screen using , press again and you should be back at the paper selection screen, which has two pieces of paper left, but they stay in their original position:
Highlight the middle piece using and select it by pressing , press or 2 times to highlight the middle option and select it with :
Pressing again will take us to the paper selection screen once more and we will highlight the last piece of paper, which is the bottom piece using and select it by pressing :
Once “inside” the paper, press or 3 times to highlight the bottom option and select it with :
Now, press and you’ll go back to the bookshelf screen. If you did everything right, a book should appear below the Washington Post and you’ll get the following achievement:
Easy, right? Good, because we will repeat this process every time we come back to the bookshelf screen, so I will list which option to select for each piece of paper with a picture as well.
Ok, now more dialog will take place, proceed to press and hold to skip everything and we will have some choices to make before getting back to the bookshelf screen. There is dialogue in between the questions, so remember to press and hold after every choice you make; the game will automatically stop skipping when it needs your input.
Before the first question, you'll get the following achievements:
These are the questions in order they appear and which option to choose for each of them:
Keep skipping everything and you'll get the following achievements in the process:
After that is done, we are back at the bookshelf screen. Highlight and select the Washington Post, press again and this time there are 2 pieces of paper to choose from.
For the top piece of paper, select the top choice by pressing or once.
For the bottom piece of paper, select the bottom choice by pressing or three times.
When you are done, a new book will appear on the bookshelf and the following achievement will unlock:
Proceed to skip the next dialogues by holding , you'll unlock the following achievement in the process:
When presented with a new question, select the third answer (探す):
Keep skipping everything, unlocking the following achievements in the process:
Now we are back to the bookshelf screen. Again, highlight and select the Washington Post which will reveal 3 pieces of paper:
For the top piece of paper, select the middle choice by pressing or twice.
For the middle piece of paper, select the middle choice by pressing or twice.
For the bottom piece of paper, select the bottom choice by pressing or three times.
A new book will appear in the bookshelf and you should also unlock the below achievement:
第３の絵本クイーンズブリッジ崩壊の真実を明らかにした。
Proceed to skip the next dialogues by holding , unlocking the following achievements in the process:
When presented with a new question, select the third answer (信じる):
Keep skipping everything unlocking once again the following achievements:
We are back once again at the bookshelf screen and as always, proceed to highlight and select the Washington Post which again, will reveal 3 pieces of paper:
For the top piece of paper, select the bottom choice by pressing or three times.
For the middle piece of paper, select the bottom choice by pressing or three times.
For the bottom piece of paper, select the top choice by pressing or once.
Another book added to the bookshelf and the following achievement is unlocked:
Back to skipping the next dialogues by holding and when presented with a new question, select the first answer this time (再生する):
Skip again and collect the following achievement:
Keep skipping until you see the bookshelf screen to highlight and select the Washington Post and reveal 3 more pieces of paper:
For the top piece of paper, select the bottom choice by pressing or three times.
For the middle piece of paper, select the bottom choice by pressing or three times.
For the bottom piece of paper, select the bottom choice by pressing or three times.
Another book and another achievement:
第５の絵本ブロードウェイ崩壊の真実を明らかにした。
Proceed to skip the next dialogues by holding and when presented with a new question, select the first answer again (読む):
I bet you know what’s next... Yes, skipping... At least there are some achievements to gain in the process:
Skip once again until we see the bookshelf for one last time (finally!) and select the Washington Post to reveal the final 3 pieces of paper
For the top piece of paper, select the bottom choice by pressing or three times.
For the middle piece of paper, select the top choice by pressing or once.
For the bottom piece of paper, select the bottom choice by pressing or three times.
The last book is added to the bookshelf and the following achievement is unlocked:
第６の絵本セントラルパーク崩壊の真実を明らかにした。
Keep skipping the dialogues leading to the end of the story, on the way, we’ll get the following achievements:
Before the end, you'll be presented with two more choices to make:
While skipping and before the last choice, we'll unlock the following achievements:
紫影の果てリリィが旅の目的地である紫影の塔に辿り着いた。
Ａのメモリー一輌だけの地下鉄の車掌Ａのメモリーを胸に刻んだ。
The last choice is finally here:
And skip until the end of the story, getting the following achievements while doing so:
リリィの世界リリィが自分の世界を見いだした。※新たな物語がEXシナリオとして追加されました。
Interesting, right?
We’re almost done! Press on the last screen and we're now back to the main menu, select the newly unlocked bottom choice (EX something):
Choose the highlighted option in the above picture to open the EX Scenarios menu, choose the only available option to go into the EX Scenario 1 chapter select. Open the only option available and skip using until it ends. When it is over, press on the last screen and the second chapter is unlocked, select it and skip again but this time you'll unlock the below achievement for doing so:
Repeat the above process for the third chapter, getting the following achievements:
Now for the fourth chapter and unlock the following achievements while you're at it:
窓越しの再会リリィが夢歩きの果てで“あの人”に再会した。※新たな物語（EXシナリオ）が解放されました。
Once you are done and back to the chapter selection screen, press 
to go back to the EX Scenario screens and you’ll see that the second scenario is available:
Fortunately this one is just one chapter long; select it and skip until the end to unlock the following achievements:
ヒュプノスの深奥イリジア３柱神の１柱ヒュプノスを撃退した。※新たな物語（EXシナリオ）が解放されました。
When it is over, go back and select the third and last EX Scenario which should be unlocked now:
This one is also just one chapter long; skip until it is over for your final achievement:
Congratulations on your new shiny completion, you earned it!
Thanks for reading and I hope we meet again soon.