Stay Loose- Agents of Mayhem has almost no penalties for failure, and no achievements or special rewards for trying to ironman your through the game. Don't feel like you need to execute every mission perfectly, or even particularly well. The game is perfectly willing to let you play in your own way, and there's nothing skippable that you can't get more of later on (you'll even be able to replay any of your past missions, once you reach the end of the story). And unlike some other open-world crime-sprees, there are an infinite number of encounters around New Seoul- you'll never run dry of loot chests to pillage and henchman to decimate. So relax and enjoy.
Don't Make Things Hard on Yourself - Another deviation in Agents of Mayhem is that there is no real penalty for switching up the difficulty. It's not tracked, it doesn't block you out of an achievement, and it doesn't take away the real ending because you didn't play the game hard enough. So if you want to conquer all four outposts but not spend the whole night doing it, or are just coming to grips with a new character or playstyle, don't be afraid to knock down the difficulty a few notches to speed things along. Conversely, if you've mastered Scheherazade or Oni, and feel like you can take down anything the game has to offer, try kicking the difficulty *up* a few levels, and seeing how far you can run with it.
Switch It Up- While LEGION lairs may get all look the same after a while, you don't have to play them the same way. It's tempting to find one team and powerset that 'works' for you, then just hang on 'til the bitter end, but you're trading fun for grim efficiency. Instead, ry out your lesser used characters, even if it means futzing with the difficulty (it ain't a sin). Also try mixing up your gadgets and powers- a few that seem weak on paper can be surprisingly effective in practice, or just bounce well off of other powers. Agents of MAYHEM is all about running with the underdogs, so don't be afraid to break out the B-team every now and again, and see what you're missing.
You can also try executing standard missions in new ways. Sure, you could take down enemy vechicles by ramming into them with your vehicle- or you could use your aerial dash to chase them down, jump on top, and roadsurf them rodeo-style until they explode from sustained close-range weapons fire. Fun is what you make of it.