I discovered all of the towers in Breath of the Wild without upgrading my heart containers:


I also discovered some
843349819196411904[/tweet]]WIKKED SPEED STRATZ, which I naturally used for cheesing the fuck out of the Akkala Tower (note that the purple gunk is supposed to block you). I was able to take the tower without killing anyone. I suspect this bug will be exploited in 100% runs of the game, at least initially, since it saves a bunch of fighting.
The Central Hyrule tower wasn't the hardest one, surprisingly, though it did require going a bit out of the way to capture. I climbed on the large hill nearest to the tower and glided onto one of the little spire things surrounding it. That gave me a chance to regenerate my stamina. I then glided to the side of the tower. The guardians spotted me, but I had juuuuust enough time to jump my way from ledge to ledge, which provides sufficient cover, then up to the top.
I cheesed Hebra pretty badly, too. I didn't have any high level cold resist, so I had to take damage. Fortunately, I have a Smash Bros Link amiibo (aka the "Link Pissing Out His Ass" amiibo) so I used that to get Epona and booked it through the mountains, gobbling down food to compensate for the heart damage. I also didn't have any fire arrows to take care of the icy structures at the base of the tower. You're not supposed to be able to jump or glide over them, but there is one part where I was able to find just enough footing on one of the blocks to pull off a frame-accurate second jump, vault over the blockade, and scale the tower.
The Wasteland tower gets a big entry in my Wall of Shame. They have a very cheap anti-cheese mechanic around the tower that causes a strong headwind to start blowing only when you start gliding towards it. The only way to actually get to that tower is to do a physics puzzle that is somehow worse than any of the ones from Half-Life 2.
It was a fun little challenge, and having all of those extra fast travel points will definitely be helpful for when I start, y'know, actually playing the game.