How do I get the memory fragment on Galata Tower?

Have you tried jumping off of a higher part of the tower, and then using a parachute to angle yourself back around? The parachute is a bit tricky, but invaluable when trying to reach odd locations like that.

I don't think I have this fragment yet, but I do think it might also be possible to jump off the top of another nearby tower to get the right angle for the parachute.

Note that you can't parachute if you're doing a Leap of Faith, so don't jump off any areas where birds are roosting or circling (or towards a haystack/rosebush/etc), lest you swan dive into a rose bush or hay bale instead.

If you're dropping down off of some impossible height, you can always press B to hookblade anything that's grabbable on the way down. No matter how far you fall, you'll always avoid damage if you can hook a platform on the way down. If you fall somewhat close to the platform, try mashing B as you fall to see if you can't grab onto it.

Hooking a platform 2 feet off the ground from a deadly fall without tearing your arm out of its socket? Ezio's all like, What? I'm an assassin. We're so bad.

Climb the Galata Tower all the way to the top. You will find a stack of hay there and birds where you usually perform a leap of faith. Stand a bit from it to avoid doing the leap and jump from the Tower. Open your parachute and maneuver it close to the tower - once you are close, drop, and that's it!