I cannot do it in the phone itself, neither in iPhoto.
How can you delete all your photos in iPhone?
How to delete all photos from iPhone
The following method is without a doubt the fastest and most efficient way to mass delete photos from your Camera Roll. You can choose to delete one or hundreds of photos at once, and get the job done in less time that it takes to say it.
1) Plug your iPhone in your Mac. Launch the application called Image Capture. You might not have heard of it before, but it comes with all Macs. It should be somewhere in your Applications folder.
Note to Windows users: I do not have a Windows machine to test this on, but if my memory is correct, you can achieve the same thing by going to “My Computer” and look for your iPhone, which should appear as cameras normally do on PC. Don’t quote me on this though. Hopefully, some commenters that have a Windows PC will be able to give us more details about that.
2) Make sure your iPhone or iPad is selected from the “Devices” list in the left navigation bar.
3) Select as many photos as you want to delete. If you want to delete all of them in one scoop, hit the “Command + A” keys on your keyboard to select all photos.
4) Click on the red delete icon at the bottom of the screen.
5) You will get one last chance to stop the mass removal of your pictures. Image Capture will ask you if you’re sure you want to delete the selected items permanently. Click Delete. All the photos will be wiped from your iPhone or iPad.