You can improve the item level of weapons or armour through magical formulae. This makes them even more powerful and can make them downright legendary if they reach a level of +24.
To increase the level of your item, you need the apprentice's formula, the assistant's formula or the master's formula. Click on a craftsman with the right mouse button, put the corresponding formula in the right field and the item that you wish to enchant in the left field. Click on confirm afterwards.
You can buy the apprentice's formula from the merchants in the starting village and in your kingdom's capital city. It increases the level of your item by one level. You can only get the assistant's formula as loot from bosses and you can only get the master's formula in the cash shop. Both formulae increase the level of your item by up to three levels.
You improve your success chances with a serendipity potion. Click on the coin symbol in the middle section of the bottom of the screen to enter the cash shop. You can simply buy the potion there. As soon as you have purchased the item, you will find it in your deposit next to the coin symbol.
If you have not used your serendipity potion yet or its effect has already been used up, you will automatically be asked if you want to use it during the next improvement.