PS4 to PS5 – Is a PSN Account Required to Transfer Data?

Judging by what I can see, the only way to delete a trophy set is if it stands at 0% total. The only other alternative is to hide trophies

Select (Settings) > [PlayStation™Network/Account Management] > [Privacy Settings]. > Sharing Your Experience > Trophies

In there you can hide games, I believe!

If you're talking about progress in the single player campaign, game saves are stored locally on the console. To transfer them from your friend's PS4, plug in a USB-Stick or external hard drive and in the main console menu go to

Settings > Application Saved Data Management > Saved Data in System Storage > Copy to USB Storage Device

There, search for your Advanced Warfare save files and copy them to your storage device. Then plug it in to the other console and go to

Settings > Application Saved Data Management > Saved Data on USB Storage Device > Copy to System Storage

and copy the files onto your own console. It's important that you are signed in with your own PSN account when you copy the files from your friend's PS4, because according to the PS4 User's Guide you need to have signed in at least once with the same account you used when you copied the saved data.

If you have an active Playstation Plus subscription, you can also upload your save data to your cloud storage and download it on the other console. To do so, follow the same steps as above, but instead of copying onto a USB device, select "Upload to Online Storage" on your friend's console and "Saved Data in Online Storage" when copying the data to the other one.

If you're talking about online progress: Your multiplayer progress in Advanced Warfare is stored on game servers online and are automatically associated with your PSN account, so you don't need to transfer save data for it manually.