Infinite Skills is a game state achieved when the duration of a skill exceeds its cooldown time. This will happen when the levels of the skill duration Ancients ( Chawedo, Berserker, Sniperino, Energon, Kleptos and Hecatoncheir) and Vaagur are high enough. (It can also be achieved without Vaagur, but that's a lot less efficient.)
After gaining access to Infinite Skills, it's still beneficial to level up the skill duration Ancients up to level 436 as they will allow you to get Infinite Energized Skills at that point.
For reference, here is a table for the levels of the skill duration Ancients needed for Infinite Skills.
|Skill||Related Ancient||Ancient level needed for Infinite Skills with Vaagur*|
|Infinite energized anything||Any of the above||436|
|Infinite energized everything||All of the above||2685|
* This is assuming that the levels of Vaagur and the respective skill Ancient are the same, although it's really not neccesary to level Vaagur beyond level 280 in order to get all 6 infinite skills. For the last row, though, you need to get Vaagur to level 1440. And it is suggested that you level the skill ancients a few levels past 2685, because of the difficulty of activating the skills.