BEWARE: An update broke several achievements, so this might unlock or not at all for you until a new update fixes the problem
This is a simple achievement, level up and perk up, but just wanted to make a point, if you level up on Harm challenges, you'll get several levels really fast, specially with more players or a highest character in the group BUT YOU WILL NOT GET ANY EQUIPEMENT.
If you want to make your life easier just level up your characters doing the other grindy achievements (Assignemts, Hives, Villain Sectors, etc ) and upgrade your equipement, do not level up fast or you'll end up with a low battle score.
Every hero has 50 abilities to upgrade in 3 different sections (Basic, Special and Master) and you'll need to level up at least to level 15 to unlock them, by the time you reach 50 you'll get all the required points.
Since every hero is different, there's no strat or recommended strat so far, upgrade what you consider according to your game style, and again, i won't recommend boosting the levels since your equipement really makes the difference in battle.