The Great Plateau in The Legend of Zelda: Breath of the Wild.
That was an effective tutorial; I agree. It very effectively taught players just how
mediocre and frustrating and un-Zelda-like this game is, by immediately making players baby an arbitrary stamina gauge, by how stupidly quickly collected weapons break, how you get every Rune one after the other (teaching the player this so-called "Zelda" game won't have a wide and varied arsenal, or dungeon items, like NORMAL and GOOD Zelda games do), and forcing the player to find towers by sight teaches them they'll have to stumble through this ugly and barren world with largely no map markers and thus no visible goals to work towards or motivation to keep trudging through this aggravating experimental disaster.
As for good tutorials in an actually great game, how about Pokémon Ruby/Sapphire/Emerald? You have to rescue Professor Birch from a wild Zigzagoon/Poochyena (depending on version), using a Pokémon from his bag.
After selecting one of Treecko, Torchic or Mudkip, you're thrust into battle against the wild Pokémon, who not only does minimal damage to you, but you can also freely learn about stat-lowering moves (Growl makes the opponent's physical moves, which is all Zigzagoon and Poochyena have at this point, weaker; Leer makes your physical moves hit harder) as well as how to lower the opponent's HP with Scratch, Tackle or Pound.
Plus, you cannot actually lose this singular fight - if you get low on HP, the Zigzagoon/Poochyena is coded to automatically flee, making it a perfect place to get a hang of this turn-based system.
It does all this without someone in-game instructing you, which is a flaw of newer games, and even FireRed/LeafGreen.
Or how about Fire Emblem: Awakening? The Prologue has the two main characters (Chrom, this game's Lord, and your just-created Avatar) up against a boss - who not only doesn't attack on his turn, but also doesn't do too much damage. You can freely get a feel for this game's movement and gameplay here, and even get a sneak-peek at pairing up if you have Chrom and Avatar stand next to each while attacking the boss. This game also has optional tutorial windows, which if you're new you can read as they appear in the first few chapters - or if you're experienced you can disable in the save's settings, with the added bonus of immediately unlocking pairing-up units, which would otherwise be locked until Chapter 3 or so (where it's actually shown with Sumia and Chrom pairing up).