"Hard Mode" is unlocked when you defeat the Wall of Flesh, the final boss of the "Normal Mode". Like all bosses, the Wall of Flesh is best handled with multiple people.
Molten Armor - made from Hellstone Bars, farmed from Hellstone in the Underworld
Accessories - Spectre Boots (Rocket Boots and Hermes Boots) and Obsidian Shield (Cobalt Shield and Obsidian Skull). The others are up to you, but you will be using a ranged weapon (preferably a minishark) to kill the boss, so boost range, defense, or magic.
Obsidian Skin Potions - made from 1 Bottled Water, 1 Obsidian, 1 Fireblossom, and 1 Waterleaf. These are your best friends!
There is lava everywhere down here. So keep using those Obsidian Skin potions to stay alive (make sure not to drown). You can take lava in buckets and bring it to the surface to make an Obsidian farm. Or you can bring down water in buckets to make Obsidian in the Underworld or other places with lava like the Underground Jungle. You will need the Obsidian and mining Hellstone to make your armor and molten items.
WALL OF FLESH
The Wall of Flesh is summoned by dropping a Guide Voodoo Doll into lava in the Underworld, which kills the Guide NPC and summons it. The Wall of Flesh always spawns in the direction you are facing and comes toward you. The Guide must be alive for you to summon the boss! Voodoo Guide Dolls are dropped by Voodoo Demons, but if it drops into the lava before you get it, it can summon the boss as well. It is better to come with the Doll and preparations made ahead of time. The Wall of Flesh takes up the whole screen and will move towards you while reaching out with tentacles and firing lasers. If the Wall catches up to you, it just pushes you in the direction it is moving. However, if it reaches the end of your world, it kills you.
So if you have a Doll and the right equipment ready, the bridge is your next step. A HellBridge is advised so you have a flat surface to run on and the Wall of Flesh chases you. You can then fire away at it with a gun, bow, or other weapon as you run away from it. If you followed my advice in other solutions, you should have a Hellevator built already, and you can build your HellBridge off of this. Make sure it is long and unobstructed so you have enough space to run on and fire away. The heads are the only part of the wall that takes damage, so aim for those and good luck!