This game got a lot of press. Having the assumption that there's not only a bazillion of reviews out there explaining every technical detail of it, but also that everyone has either read up on or played it already, I'm going to skip the minute descriptions of BOTW's gameplay and get right to my opinions on its various aspects. I won't talk much about the story, there isn't very much to it anyways, but there's a mention that can be considered a spoiler. FYI.
Playing Breath of The Wild felt like an adventure, very much similar to classics such as Wind Waker and Ocarina of Time. The whole open world meme is overrated if you ask me, I didn't even like Skyrim. What this one got above Twilight Princess and Skyward Sword is that it doesn't force fetch quests on you at all angles. The really brilliant aspect for me is the clever use of physics, which is admittedly possible because there are no borders in the game. Even with only 4 tools and all those shrines, the puzzles never grew on me and every shrine was interesting in its own way. Lots of games build on top of physics engines don't do anything of signifiance with them, so seeing that aspect utilized in so many ways in just one game is quite impressive.
Exploring the overworld still got old when I reached a point where both Korok seeds and proof's of conquest started getting useless as I had enough resources on me. The game is fun and immersion invoking the way it is, but there's room for more. Personally I would have loved to explore structures such as caves and dungeons, yet despite the ability to freeclimb the game feels really level since you there's only fields and mountains.
I'm not a huge fan of the combat because of the insane amounts of HP some enemies have. Obviously that's to encourage the use of tools and environment, but it's pretty tedious in situations where you can't really use either. Lynels are just the worst. They take forever to kill so you're guaranteed to get really good at fighting them eventually, but without proper preparation they're still packing too much. My guess is you're supposed to fight them with some preparation, however neither holding on to strong weapons and attack power amplifying food are good options imo. The former means you'll take longer to kill the weaker enemies, which also have considerable amounts of hitpoints, and the latter requires you to make use of the cooking system. The cooking system is kinda awful. It would be tolerable if the game saved recipes the player discovers and let them select those for quickly selecting the right ingredients, but as it is I never enjoyed navigating through dozens of menu icons and selecting multiple pieces to prepare a single meal.
The story is rather thin, and that's great. Gameplay is the focus over cinema, an aspect I almost didn't aspect considering the industry today. Beyond that I really don't know what to make of the story, though. The setting with machines getting taken over by ganon is just too weird. Apparently Ganon is a virus now - so can we expect a Mega Man X crossover next...? And none of this gets explained ever. The memories are merely Zelda fanservice and don't really tell you anything you can't learn elsewhere. Finding those should have been a sidequest. If you ask me.
Putting the main story aside the game could have done without the numerous sidequests. The shrine quests are all fine, but does a hero really need to help random people with doing their shopping? Is that fun and interesting? Does it serve the world building? Problem none of it, it's filler content to make the game appear meatier than it is. Quest rewards are kinda awful too - it's mostly just potions and meals you could concoct or cook yourself. At least the few quests that come with useful rewards mention this so it's easy to ignore a lot of the filler.
Despite me bickering a lot here I had a blast playing this for multiple dozen hours. Exploring the expansive world is a real adventure in itself, the game looks great that you forget you're playing on a comparatively underpowered machine, music and sound are a perfect fit, the few main quests work very well and don't take away your freedom to explore too much. Highly recommended. A must play for Zelda fans, even if they feel the game changed the formula too much. Breath of The Wild, despite a lot of shortcomings, is leaps and bounds above Skyward Sword.