This achievement is awarded for saving The Chief at the end of Stage 6 as Zan on single player. This can be done on Normal difficulty and higher on the US/EU version of the game, or Easy and higher on the Japanese version. For some reason the game is cut short on Easy in the US/EU version.
To do this, after you press down on the elevator for the first, time head right. Kill the gun mobs and enter the middle door. You will be attacked by a few waves of enemies. Once you have cleared the room of enemies, destroy the switch (large computer panel) on the right side of the room, after you do this you will be exited back to the hallway.
Kill the two respawned enemies, then head back left again to the elevator and press down again, head right again to enter another hallway of doors. You will be attacked by another group of 2 fighting mobs, dispatch these then head into the middle door again. Same as before you will get a few waves of mobs, kill them and destroy the panel on the right as you did in the previous room.
You will again be exited to the hallway after this is done. After killing the respawned enemies, head back left, punch up on the elevator once, you're now back to the first hallway of doors. Sprint right to find the chief tied up, approach him to free him. There is a bomb planted on the floor the chief is on, you can see the timer for this on the red canisters on that level. You need to complete the above before the bomb goes off.
You will then have a boss fight on the roof with a Jet pack boss and Jet pack mobs. Fly kicking is your best bet, throw in some of Zan's charge ability when you can. (Double tap forward then press punch to land the attack)
Don't worry that your achievement hasn't popped yet, it pops at the beginning of the next Stage for some reason.