This is what the Labyrinth looks like on the Magic Map
Inside the Labyrinth, you can find Minotaurs, Maze Slimes, and Fire and Slime Beetles. Minotaurs have a chance of dropping a Maze Map Focus, which can be crafted into a Maze Map which makes navigating the Labyrinth much easier. They can also make Uncrafting Tables, which allow you to uncraft an item back into its base ingredients.
The Labyrinth is made of Mazestone, which is very slow to mine. There are also traps and loot galore, so be sure to grab what you can carry.
Killing the Minoshroom will net you a Minoshroom Trophy and some Meef Stroganoff, as well as the treasures in the chests. Eat the Meef Stroganoff to be able to enter the Fiery Swamp at the center of the Twilight Swamp.
This is what the Hydra looks like on the Magic Map
The Hydra is a giant multi-headed dragon that breathes fire and spawns in the Hydra Lair, which is at the center of Fire Swamps.
Once defeated, the Hydra will drop Hydra Chops, a Hydra Trophy, and Firey Blood, which is one thing needed to gain access to the Highlands.