It is advised to be level 30 with somewhat good gear before you even begin to tackle the hard more bosses, because even the first of the three hard mode bosses will give you a challenge. Even at level 30, the bosses have a 5 level advantage over you.
All the hard mode bosses can drop a lot of cool stuff, including pets, Recipes, weapons, equipment and rare building materials.
Anyway, in order to summon the hard mode bosses you will need an item. Each boss has its own item that you need to craft in order to summon it, and the following three items allow you to summon the three hard mode bosses:
1) How to summon the Ancient Evil Electro Worm (hard mode version of the Ancient Worm)The Ancient Evil Electro Worm is the first of the hardbosses, and you need to craft an item called the Relic of Thunder to summon him. But before you can do that you will need to get the Recipe for the Relic of Thunder, which is a rare drop from the Ancient Worm - the non-hard mode version of the boss. This should be easy to farm since the boss is only level 10, but you will need a bit of luck to get the Recipe.
Once you have the Recipe for the Relic of Thunder, craft it at the Alchemy Table for 4 x Energy Crystals and 16 x Electro Quartz. This creates the one-time use Relic of Thunder. Use this to create/spawn an event that pops up on the map with its own island. Go to this island to fight the Ancient Evil Electro Worm.
2) How to summon the Arctic Dragon Countess (hard mode version of the Dragon Queen)In order to be able to fight the Arctic Dragon Countess, you need to craft and use a Relic of Frost. But first you need the Recipe, which is a rare drop from the Dragon Queen. When you have the Recipe, collect and bring 4 x Energy Crystals and 16 x Sea Sapphire to the Alchemy Table to craft a Relic of Frost.
Use the Relic of Frost to spawn an event with an event island that allows you to fight the Arctic Dragon Countess.
3) How to summon the King of Light (hard mode version of the Hollow King)Begin by grinding the Recipe for Relic of Light from the Hollow King. When you obtain that, get 16 x Sun Diamonds and 4 x Energy Crystals to the Alchemy Table.
This allows you to craft the Relic of Light, a consumable item that begins an event with its own island. Go to this to fight the King of Light, the third and final hard mode boss.