Found a really good way to earn this achievement. It requires you to maintain 10x multiplier in 10 chapters (doesn't have to be different chapters) in Arcade Mode.
Load up Act II chapter VII on casual or normal, as soon as you take control of your character run to the turret at the back-right of the ship. Shoot down the 2 gas barges that pop right in front of the turret. Now head over to the front of the ship, a reaver will pop on the right side, shoot it down with your lancer. Another reaver will pop to the left of the ship, shoot it down with your lancer as well.
Next part is a little bit tricky and might take a few tries to get the timig right, but grab the turret on the front-right of the ship. You'll see a gas barge pretty far away, wait till it's closer and turns a bit to your left. Shoot it down, aim a little in front and above it.
As soon as it dies, head to the front-left turret, you'll see another gas barge heading straight for you, wait untill it's pretty close because this kill will give you the 10x multiplier and if you get hit by any of the reavers flying around after your gas barge kill you will lose your 10x multiplier and there will be no chance to regain it, if this happens you must reload your last checkpoint.
A cutscene will play shortly after the last gas barge and as soon as you get control of your character you must take cover by the edge of the ship so you don't get hit by any of the lights.
This chapter takes about 2:45 to complete.
Check out my video for it.