To level up fast in Elex 2, you need to have Experience Points (Exp). To get the Exp, you need to play the game and win battles and missions.
Especially, at the beginning of the game, it is advisable to do as many side quests as possible. Avoid tough enemies such as with the crossbones symbol and find companions immediately so that they can help you in inevitable battles. Even if your companion does all the work, you’ll get the Exp for completed battles.
In Elex 2, you’ll find some potions that can help you greatly when leveling. A small potion will give you 500 exp, a medium one gives you one Attribute Point and a large one gives you one Learning Point (LP). You can also make the potions yourself. There are also potions that permanently increase a certain attribute such as the warrior's potion (+1 strength). If you can't make the potions yet, you can occasionally find them as loot in the open game world.
As you progress through the game, you may encounter attribute trainers such as Eva who can be found in the Clerics’ Castle, can give you 10 attribute points for each level of "Attribute Points". And with the "Attribute" ability, you get an extra attribute point every time you level up. "Experienced Hunter" gives you more Exp for killing opponents and "Practitioner" will give you exp points for completing quests. All of these skills require a certain level of intelligence and cunning.