Upgrading your Hero is crucial, and a great way to do this is to use the Skill Tree. You will find a number of upgrades that you can unlock to make all of your heroes permanently stronger. 

There are two branches in the Skill Tree, one of which uses coins to unlock upgrades, and the other of which has fewer but more powerful upgrades. This other branch uses Alien DNA to unlock the upgrades. These can be found by completing trials.