Can I downgrade my iOS 9 back to iOS 8.4?

Did you upgrade to the Public Beta? If so, you must first erase the beta software, then re-install the latest shipping version of iOS, and finally restore from your previously saved iTunes backup.

how to erase a beta software from my iphone?

Follow these steps:

1. Make sure that you're using the latest version of iTunes.
2. Put your device in recovery mode and restore it. If you turned on Find My iPhone, enter your Apple ID and password after the restore to activate your device.
3. If you can't finish the restore, get help.
4. After the restore is complete, you can set up your device from your archived backup. This backup should be from an earlier version of iOS.

This does not actually work and I'm not sure why Apple has an article on downgrading.

The beta is VERY clear about upgrading a device to beta software, this cannot be undone.

• This version of iOS is intended only for installation on development devices registered with the Apple Developer Program. Attempting to install this version of iOS in an unauthorized manner could put your device in an unusable state, which could necessitate an out of warranty repair.
• Devices updated to iOS 9 beta can not be restored to earlier versions of iOS. Only registered development devices will be able to upgrade to future beta releases and the final iOS software.

What you say is definitely the official stance when it comes to the Dev Beta.

For the Public Beta though, Apple explicitly does offer support for "downgrading to shipping versions", which was why that was my first question to the OP.

Quoted from the FAQ for the enrollment in the Public Beta program:

"How do I get a shipping version of iOS back on my iPhone, iPad, or iPod touch?

.... If you would like to go back to a previously released version, you must first erase the beta software, then re-install the latest shipping version of iOS, and finally restore from your previously saved iTunes backup.
Learn more about how to erase and install iOS
Learn more about restoring from an iTunes backup

"

My post above is basically just a copy/paste of the relevant steps from that first link - perhaps also the article you are referring to?

{EDITED: I initally quoted from the wrong section)

You can downgrade ios dev beta to latest signed version of the firmware - this downgrade option has been available for sometime - Steps:

1) Download latest signed version of firmware (currently IOS 8.4)

2) Backup IOS Device to iCloud

2) Connect IOS Device to iTunes

3) Put IOS Device in DFU mode (Hold Sleep & Home button for exactly 10secs then release sleep button still holding home button until iTunes pops up saying phone is in recovery mode)

4) In iTunes press ALT key and select recover option

5) From file selection select the latest signed version of firmware downloaded in step one

6) Once recovery is complete set up from icloud backup

7) Done

You can't downgrade the WatchOS - The only way to remove the Dev Beta from the watch is to take it into Apple Store and they will send it away to get version 1.01 flashed back - This is because there is no DFU mode on the watch.

I don't like to ios 9