Story-related and cannot be missed.

At the end of the game, you will need to help Osgood at the Wester Drumlin location.  First, you will need to access the surveillance cameras at the property; the codes to unlock them have been phoned in to you throughout the game.  In case you didn't write them down:

Shark: 1747
Watcher: 9327
Angel: 5801
Joker: 9226

Once you've set up the cameras, you will have a small timed section where you will need to delete a photo of Mr Flint from the phone's texts.  After that, you will watch what goes down at Wester Drumlin. Eventually you will be able to text Osgood again and once you send her a few messages, this trophy will unlock.

MISSABLE

Note that this trophy will unlock after the game's credits, because the hidden ending consists of cutscenes after the credits.

The six tasks are as follows:

1) Successfully destroy the Weeping Angel on the phone before it reboots into safety mode (see There's something on the phone! for a breakdown on that).
2) Convince Marguerite to send you a new download link for the MET Archives (Master persuader ), scan the full video (Wibbly wobbly… time-y wimey… stuff ) and upload it to Osgood.
3) Find all four TARDIS pictures and upload them all to Osgood (Not your average police box ).
 

Story-related and cannot be missed.

After uploading more clues to Osgood, you'll eventually decide that Wester Drumlins deserves more investigation and Osgood will send a coworker there. The next time you access the home screen, Mr. Flint will call. Once you've completed the call, the trophy will unlock.

After this phone call, you will have a short exchange with Osgood.  After that exchange is when you will want to back up your save, to give yourself another chance at the one-shot skill check that will dictate whether you can stay on the path to the best ending and therefore Happy ever after... .

MISSABLE

You first need to unlock Master persuader , in order to access all of the files you can download from the MET Archive. Once you've done so, go into the phone's Gallery, then the downloads folder. Play the video located there and once you have, this trophy will unlock.

Story-related and cannot be missed.

Late in the game, you will be able to access the Private folder in the Gallery.  Play the bottom middle video, scan it, then upload it to Osgood. Once you've done so, you'll unlock this trophy.

MISSABLE

Early in your investigation, you will download some files from the MET Archives. That will use up your one remaining download of those files. If you want to get the game's best ending (and therefore Happy ever after... ), you will need to get the download link sent to you again so you can download all of the files instead of just the few needed to get through the game.

To get another download link, you will need to call the MET Office (phone number 020 7946 0827) then enter 3 (you must hear the option first), then enter extension 1034 after the beep.  This will connect you with Marguerite but you will not be able to communicate with her. You can do this part at any point in the game prior to uploading the corrupted video file from the Downloads folder to Osgood.

Marguerite will then text you once you've uploaded said video file. Via text, you need to convince her that you are Lawrence and get her to send you a new download link. Choose the following options:

Sorry, I've got a problem with the file you sent me
We met last week
It was good to meet and chat in your office
Yes, the old video footage
I accidentally deleted it :(
Fantastic
Can you give that to me too?

Story-related and cannot be missed.

Midway through the game, you will be able to access the Wester Drumlin folder in the phone's Gallery. Once in there, you will need to piece together a puzzle made of glitchy puzzle pieces, which will give you access to the Wester Drumlin photos.  Scroll through all of them (scanning one on the way) and then back out of the folder. This trophy will unlock soon after.

After unlocking this trophy, there will be a timed segment of the game. There's no timer on screen; the phone will just gradually turn gray, until it reboots into safe mode. You need to get the following done before the game reboots into safe mode; failure to do so will lock you out of Happy ever after... (you can still finish the game if you reboot into safe mode but you will need to do another playthrough for Happy ever after... ).

You will need to destroy all four corrupted data pieces.

First you need to talk to Osgood. She will unlock the ability to destroy the corrupted data - it works the same as scanning, except you need to spam  to fill the bar instead of just holding it down. Only this time you will be interfered with while doing so.  After clearing one corrupted data piece, Osgood will message you; just ignore her, as it is unnecessary and will just waste time.

1) Browser: The Into the Unknown bookmark - Click the moth picture, then the word "CUBE", then "no", then "I have my own path", While deleting the glitched picture, you will have to deal with some pop up windows - click "not interested", "I'm fine thanks" and "proceed").

2) Gallery: The Till Death Do Us Part album - The fifth picture (glitchy). You'll be sent to a few other photos during the process; just back out of the photo and go back into the glitchy photo to keep working at it.

3) Mail: The findme.web email - The glitched part of the message. Midway through, all of the emails will disappear and their orders will switch around - this is randomized so just click each bar until you find the glitched email again and continue to destroy it.

4) Chat: In Mo's message. Scroll up until you find the glitched part.The first few interruptions will put you into different parts of the message so you'll have to find your way back to the glitched part. The final interruption will bring up a ton of pop up windows; just close out of each of them before continuing to destroy them.

Once you have destroyed all four corrupted data pieces, go back onto the Home Screen.  You will need to destroy the Weeping Angel on the home screen. Once you've done so, the timer will stop (you should notice that the screen returns to normal).

Story-related and cannot be missed.

Late in the game, you will be able to access the Private folder in the Gallery. The last video clip in the folder is from the actual Don't Blink episode of Doctor Who; just watch it and you'll unlock this trophy.

This can also be scanned as a clue and sent to Osgood so I'm fairly certain it's a requirement to finish the game.

Story-related and cannot be missed.

The bulk of the game involves searching the contents of the phone for pictures, texts etc. for clues to Lawrence's disappearance, then scanning them over to Osgood.  Once you've scanned your first clue, this trophy will unlock.

Story-related and cannot be missed.

Once you've gained access to Lawrence's text messages, simply open Mo's text and scroll down until you reach an audio message. This is a scannable clue and once you play and scan it, you'll unlock this trophy.