This achievement can be earned in:
-Online Multiplayer
-Local Multiplayer
-Local Single Player
Apparently, the achievement require to have way less than 10%. In fact, you need to have less than 1 rectangle of energy left. You'll understand when you'll have the right amount of energy when you'll hear a short "zzzing" sound.
The easiest way to earn this achievement is, of course, by boosting.
If you have 2 pads you can earn it in local multiplayer.
First of all, from the main menu go to Gameplay Settings and set match time to OFF.
Then go to multiplayer, versus, select the caracter you prefer, and as your rival select GREEN ARROW.
Lower your main character energy down untill you have just one bar left, then start shooting arrows with green lantern by pressing B. Once Heard the "Beep", beat the crap out of green arrow, and earn the achievement.
It's not necessary to turn match time off, especially if you use transitions to lower your energy (during transitions, times stops).