How to do I upgrade my skills level to attack higher level monsters?

Making your legions stronger comes from more troops and more / stronger heroes. Make sure you complete research for the legions and try to unlock the slots for the 2nd (and eventually 3rd) hero slot. Assign your best heroes to the legion and in the Hero menu find them and use wisdom medals to unlock and upgrade the skills.

Tap on any hero in the hero menu and at the bottom tap on the scroll icon to open the skills list. You can tap on any skill to see its effect and the requirements for unlocking it or upgrading it.