How to delete photos permanently

The short answer: delete the photo, then delete it again from Recently Deleted (iPhone) or Trash (Google Photos), then remove the copies in chats, shared albums and backups. Tapping delete once only moves a photo to a holding area.

iPhone

Delete the photo in Photos. Then open Recently Deleted under Utilities, unlock it, tap Select, choose the photo and tap Delete. Items otherwise stay there for about 30 days. With iCloud Photos on, this removes the photo from iCloud and your other Apple devices too.

Android

Google Photos: delete the photo, then open Collections, then Trash (sometimes called Bin), and choose Delete permanently. Backed up items stay in Trash for about 60 days, others for about 30. "Delete from device" is different: it frees space on the phone but keeps the cloud copy.

Samsung Gallery: empty the Recycle bin from the Gallery menu, and check any cloud service Gallery syncs with. Menu names vary by manufacturer and version.

The copies people forget

Chats. The photo is still in the conversation and often in the app's own media folder.
Shared albums. These hold separate copies. Remove the photo from the album.
Edits and screenshots. Each one is a new file.
Backups and computers. Old phone backups and automatic imports can keep copies for years.
Other people's phones. Anything you sent is theirs now. "Delete for everyone" helps only if they have not saved it.

Doing these in the same order each time is the easiest way not to miss one.

Deleting from a hidden or locked place

The same holding areas apply. On iPhone, deleting from the Hidden album sends the photo to Recently Deleted like anything else. Google Photos Locked Folder works differently: items deleted there are generally removed straight away rather than sent to Trash, and if Locked Folder backup is off they exist nowhere else. Samsung Secure Folder has its own Gallery with its own Recycle bin, so empty that one from inside Secure Folder. Inside a vault app, check how deletion works before relying on it. In VaultWell (coming soon), items you delete inside a vault are removed from it; the original you imported from Photos is a separate copy you delete yourself.

Is it really gone?

Modern phones use encrypted flash storage, so a file removed from trash is generally out of reach of everyday recovery tools. Specialist forensic tools are a different matter and depend on the device and situation. No app can honestly promise more than that.

If a photo might be evidence in a legal matter, deleting it could cause problems. This is general information, not legal advice; speak to a lawyer first.