Doki Doki Literature Club Plus! (UP)

As of right now, this achievement is still unobtainable. I decided it would be good to go ahead and have a guide ready for when the upcoming update fixes it. Once the achievement is obtainable, I'll come back and edit any of this as necessary.
EDIT #1: This achievement is now obtainable!
EDIT #2: As Vudix mentions in his solution above, this achievement is only obtainable seemingly if you had 100% data collected BEFORE the more recent patch. The secret poems obtained in Act 2 are reportedly not equally being distributed, causing some to not appear at all for several players. If you had all the secret poems already, you should still be able to find the other images and get to 100%. If you didn't, you'll likely have to wait for a patch.
EDIT #3: A patch has been released that fixes the RNG issues of the secret Act 2 poems. Special shoutout to Vudix for submitting tickets and keeping us all up to date on what's been going on!

To collect all of the data available, you will need to unlock all of the hidden images available in the game, and listen to every song playable on the music player. To check your progress, you can view your data collected percentage on the desktop settings screen.

The following is a list of all the images, and how to unlock them. Please keep in mind, there will be spoilers.

Wallpapers
Image #1-7: These images are already unlocked when you start the game.
Image #8: Complete the Side Story “Trust 1”
Image #9: Complete the Side Story “Respect 1”
Image #10: Complete the Side Story “Understanding 1”
Image #11: Complete the Side Story “Trust 1”
Image #12: Complete the Side Story “Balance 2”
Image #13: Complete the Side Story “Respect 2”
Image #14: Complete the Side Story “Understanding 2”
Image #15: Complete the Side Story “Balance 2”
Image #16: Complete the Side Story “Reflection 2”
Image #17: Complete the Side Story “Respect 2”
Image #18: Finish the Poem Mini-Game in under 20 seconds.
Image #19: Select the word "Kawaii" during the Poem Mini-Game.

Poems
Image #20: View Sayori's first poem. This can be obtained in any kind of playthrough.
Image #21: View Sayori's second poem. This can be obtained in any kind of playhthrough.
Image #22 & 23: Complete both parts to the side story "Trust"
Image #24: View Natskui's first poem. This can be obtained in any kind of playthrough.
Image #25: View Natsuki's second poem. If you specifically only pick words for Yuri and side with her on Day 1's argument, Natsuki won't want to share poems with you. To avoid this, include some words for Natsuki on your poem for Day 2, or simply ask for Sayori's help during the Day 1 argument.
Image #26 & 31: Natsuki's and Yuri's third poems respectively, written about a beach. To get this, you need to make sure you're still on speaking terms with Natsuki and Yuri, while also not specifically only writing poems for either one. On the third day, both of the girls will write poems on the same subject. You can only view these both if you haven't exclusively written poems for Yuri or Natsuki, while also including a few words for them both during the Poem Mini-Games.
Image #27: Natsuki's special poem. You will receive this if you write all three poems for Natsuki in Act 1.
Image #28: Complete both parts to the side story "Balance"
Image #29: View Yuri's first poem. This can be obtained in any kind of playthrough.
Image #30: View Yuri's second poem. Similar to Image #25, except it's the same way for Yuri. Just say on good terms with her by not only picking words for Natsuki, or picking a side on Day 1, and you should get this one.
Image #31: See the instructions for Image #26.
Image #32: View Yuri's special poem. You will receive this if you write all three poems for Yuri in Act 1.
Image #33-38: These poems are part of the story that you will be able to view regardless of your actions. These images include all three of Monika's poems during Act 1, an... interesting poem that Yuri writes for you in Act 2, an altered version of one of Monika's poems in Act 1 that you get in its place during Act 2, and a poem written for you from Just Monika in Act 3.
Image #39: View Dan Salvato's special note at the end of the game. You'll have to get the "Good Ending" of the game to see this. For more detailed instructions, see the guides for the achievement "Dan says hi"
Image #40: View Monika's final message to the player. This can only be done by getting the "Bad Ending of the game. Essentially, run through the game and never save and you should get this, or just play normally if this is your first time.
Image #41: I'm still searching for specific instructions on this one, but I believe this is unlocked once you view Sayori's poem on the day of the festival. I don't remember having to go out of my way to figure out how to get it, so for now just focus on getting all of the other poems and you should find that this one is unlocked for you. If anyone can confirm the process for this one then that would be stupendously helpful!
Image #42: View Natsuki's Act 2 poems. The first one you can obtain by writing two poems for Natsuki during Act 2. She will then give you a poem called "Open Your Third Eye" however it is written in the code of Base 64, so it won't look like anything that you could read. The other poem you should receive on the fourth day of Act 2 regardless of your choices. This isn't a poem, but a warning written by Natsuki about Yuri's erratic behavior.
Image #43 & 44: View all of Yuri's and Monika's Act 2 poems. You should get these regardless of your actions.

CGs
Image #45: Write a poem for Sayori.
Image #46: Write a poem for Yuri.
Image #47: Write a poem for Natsuki.
Image #48: Write two poems for Sayori on Days 1 and 2.
Image #49: Write a second poem for Yuri. (Same playthrough as Image #46)
Image #50: Write a second poem for Natsuki. (Same playthrough as Image #47)
Image #51: Choose to help Yuri prepare for the festival in Act 1.
Image #52: Choose to help Natsuki prepare for the festival in Act 1.
Image #53: Tell Sayori you love her after she reveals the truth to you.
Image #54: Complete Act 2 and begin Act 3.
Image #55: Complete the side story "Trust 2"
Image #56: Complete the side story "Understanding 2"
Image #57: Complete the side story "Respect 2"
Image #58: Complete the side story "Balance 2"
Image #59: Complete the side story "Reflection 2"
Image #60: Complete the side story "Self-Love 2"
Image #61 & 62: Complete the side story "Equals." This side story is unlocked after completing both parts to all six side stories.


Secrets
Image #63-71: When you start the game from the Desktop part of the actual game, it predetermines 3 out of 11 secret poems that you will come across in Act 2. There are nine poems you need to find, the other two do not count towards the achievement. These two in particular are images of a poorly drawn Sayori hanging herself (called Happy Thoughts) and another is a corrupted image of Monika. One poem in particular will ask you to stare at a certain part of the screen. Do so, it isn't a jump-scare (I promise I would not do that to you) or you can look away if you're really paranoid. Either way just wait until it automatically goes to the next page. These images will require you to play the game a couple of times, but thankfully using the skip dialogue options you can speedrun to the points you have to get to really quick. Check your three images, if they were new, great, if not, restart the game and try again until you have all nine secrets. (Note: Saving and reloading right before a secret poem appears does NOT change which poem you will get. The script makes it so that the same poem will appear in the same place until you reboot Doki Doki Literature Club within the game.)
Image #72: During Act 2, quit out to the desktop and continually come back in to the Doki Doki Literature Club start screen. You'll need to view a rare start screen occurrence, you'll know it when you see it. (Note: This isn't about the secret warning messages you can get when starting up the game, although these are pretty amusing and make finding the secret start screen a bit more tolerable if it's taking awhile.) EDIT #1: There is a 1/64 chance of obtaining this secret start screen. You have to get to a point after Monika glitches your screen while in the classroom before you can begin trying for it. Do NOT force quit your game after seeing it, click the A button or else it doesn't count. Thanks to Spiderboy11711 for this info!

Backgrounds
Image #73-84: All of these images are unlocked by viewing different locales in the main story and side stories. Therefore, focus on getting all of the other images and by the time you're done you should also have these unlocked by extension.

Sketches
Image #85: During the Poem Mini-Game, select the word "Doki-Doki"
Image #86: During Act 1, when presented with your choices for who to help over the weekend, attempt to pick both Sayori and Monika before making a choice between Yuri or Natsuki.
Image #87: Delete Monika's character file in the browser before starting a new game. (I might be wrong, but I think you have to beat the game at least once to do this. See the achievement "Two Stocked" for more info)
Image #88: Write a perfect poem for Natsuki, choosing only words she likes in the Poem Mini-Game.
Image #89: In Act 1, write all three poems for Natsuki.
Image #90: Write a perfect poem for Sayori, choosing only words she likes in the Poem Mini-Game.
Image #91: In Act 1, write all three poems for Sayori.
Image #92: In Act 1, on the day of the festival, save your game. Save again before walking into Sayori's room just to be sure. Once you find Sayori chilling out in her room and your character begins to panic, attempt to load your saved game before continuing to Act 2. EDIT #4: See II Caitlin M II's comment below if this isn't working for you.
Image #93: Write a perfect poem for Yuri, choosing only words she likes in the Poem Mini-Game.
Image #94: In Act 1, write all three poems for Yuri.
Image #95: As soon as Act 3 begins, you will see Monika across from you at a table. Once you see this exit to the desktop as soon as possible, and delete her character file from the browser. Go back into the game and continue on.
Image #96: Unlocked after viewing an email that you will receive while pursuing other images.
Image #97 & 98: View Dan Salvato's special note. See Image #39 or the guides for the "Dan says hi" achievement for more details.
Image #99: In Act 3, Monika will begin to loop into randomly selected dialogue. When this begins, attempt to hit the skip button under the dialogue box.
Image #100: In Act 1, on the first day of sharing poems, Natsuki and Yuri will begin bickering back and forth. When they turn to you for your opinion on who's right, ask Sayori for help.
Image #101: In Act 1, after the second day of poem sharing, Sayori will ask you if you'd still walk home with her if another one of the girl's asked to walk home with you instead. Tell Sayori you would still walk home with her.
Image #102: View the file "poemwords.txt" in the desktop browser.
Image #103: Write two poems for Natsuki in Act 2.
Image #104: While in Act 2, select a corrupted word in the Poem Mini-Game. The word won't look like any form of English to be certain.

Promo
Image #105-107: In Act 1, write a different poem for a different girl each day.
Image #108: In Act 3, listen to 15 of Monika's randomly selected lines of speech. For more details see the guides for the "She Will Never be Real" achievement.
Image #109: Get all of the secret images listed above from Act 2.
Image #110: After Yuri kills herself in Act 2, do NOT hit the skip button. Instead, continue loading autosaves until you reach the point in the story when Natsuki shows up after the weekend is over.
Image #111: Finish all seven side stories.
Image #112: Select the word "horror" in the Poem Mini-Game.
Image #113: Delete Monika twice.


Music
To unlock all the music, just do everything else listed for the images. You'll get all the music as you go. Save for ONE track, "Candy Heartz" (Heartz with a Z). A similar track called Candy Hearts (Hearts with an S) should already be available. Listen to Candy Hearts a few times, and Candy Heartz should unlock.


And that should be everything. You DO NOT need to view all the secret files in the browser at specific times, as some rumors have stated. Like I said, when this achievement is obtainable I'll come back and edit any of this information as needed. Happy hunting!

Confirmed bugged at this time based on two players giving me solid feedback. I already forwarded a comprehensive bug list of issues; the save wipe glitch and the current 98% glitch with this achievement. Will post here with a patch date; at minimum; a notice when it hits QA.

Edit 1: Sent to QA.

Edit 2: Patch will be live this week. (Posting this edit as of July 14th.)

Patch is live as of July 16th.

Edit 3: This achievement may be discontinued. All users who did not exceed 100% before the patch may not be able to get it. The trigger is Test VM only; but some images may never appear due to an RNG issue. I spoke to Mithost from Serenity Forge/Team Salvato and they confirmed there’s an RNG update on the way that consoles have not yet received.
(Patch is on the way)
So far I’ve heard testimonies from 4 players and seen several in the comments that did not have 100% before the patch. Are you in the same boat? Let me know!

For reference; I attempted for 10 hours straight without getting any new notes. Using Reset.sh between attempts.
Others like Dwaggienite tried for 11 hours+ with the same result.

Edit 4: Patch to fix RNG will drop soon. (Posted as of July 23rd) It has already been submitted to QA.

Edit 5: Patch dropped, RNG should be fixed.

I will leave this solution up as a record of previous fixes and maintain it as a place to drop your comments. Post if you still have issues obtaining the achievement so I can look into it. Please refer to my friend Sir Noncy’s guide for a proper guide on this achievement. Send any likes you would put on this solution to his solution. Thanks.

Confirmed bugged at this time based on two players giving me solid feedback. I already forwarded a comprehensive bug list of issues; the save wipe glitch and the current 98% glitch with this achievement. Will post here with a patch date; at minimum; a notice when it hits QA.

Edit 1: Sent to QA.

Edit 2: Patch will be live this week. (Posting this edit as of July 14th.)

Patch is live as of July 16th.

Edit 3: This achievement may be discontinued. All users who did not exceed 100% before the patch may not be able to get it. The trigger is Test VM only; but some images may never appear due to an RNG issue. I spoke to Mithost from Serenity Forge/Team Salvato and they confirmed there’s an RNG update on the way that consoles have not yet received.
(Patch is on the way)
So far I’ve heard testimonies from 4 players and seen several in the comments that did not have 100% before the patch. Are you in the same boat? Let me know!

For reference; I attempted for 10 hours straight without getting any new notes. Using Reset.sh between attempts.
Others like Dwaggienite tried for 11 hours+ with the same result.

Edit 4: Patch to fix RNG will drop soon. (Posted as of July 23rd) It has already been submitted to QA.

Edit 5: Patch dropped, RNG should be fixed.

I will leave this solution up as a record of previous fixes and maintain it as a place to drop your comments. Post if you still have issues obtaining the achievement so I can look into it. Please refer to my friend Sir Noncy’s guide for a proper guide on this achievement. Send any likes you would put on this solution to his solution. Thanks.