Steel Haven Hero
Complete the story
Finish the story mode with any of the three main characters. Easy difficulty works. It will unlock an additional hero "Jackson".

Action Jackson
Complete the story playing as Jackson
Complete the story mode once again playing as "Jackson". And Yes you will have to play all the locked levels from the beginning, unlike with other heroes.

Harder Than A Coffin Nail
Complete the story in hard mode
Set the game to Hard mode from the settings screen. This can be achieved in the second playthrough while playing as hero "Jackson".

Cooperation Makes It Happen
Complete the story in co-op mode
If you have a friend who likes Beat 'em up games and can help; plug in an additional controller and complete the story in Hard mode while playing Jackson with any of the three main Heroes in your second playthrough.

Both Sides of The Story
Get both game endings
After beating the final boss "Freya" the game will give an option to either SPARE or KILL her. You can choose to SPARE her in your first playthrough. In your second playthrough as "Jackson" select the option other than what you had chosen in your first playthrough. Or you can take a shortcut and just load the final boss level with any of the three main Heroes as soon as you complete your first playthrough.

Relay Rage
Complete the story in relay mode

I’m a Survivor
Beat 100 enemies in survival mode
Beat 100 enemies in any of the survival mode levels. This can be achieved easily in local co-op mode with a friend.

A True Maverick
Shoot down 500 enemy aircraft in survival mode
Shoot down 500 enemy aircraft as the jet fighter in survival mode. No co-op option is available here. You will have to do it solo.

Below two are the toughest achievements in the game. I suggest you try these on Easy Difficulty.

Not Afraid of Freya
Beat the final boss without getting hit [0.9% of players have this achievement]
Even on easy difficulty avoiding getting hit by Freya's power moves and countless goons is almost impossible. Test your skill!

Indestructible
Don't lose a life in a single play through [1.0% of players have this achievement]
Try to get this in co-op mode. Still, you have to be very careful during fights and don't miss health pickups, use them wisely.