For this achievement you must obtain at least 1 star on all 14 original echoes in Echoes Mode.
Echoes Mode is basically a replay of a portion of a specific level of the game. The goal is to get a high of a score as possible.
The main motivators for your score are beating the "target time" and amassing different skill shots during your Echo run (try and use as many as possible, as newly used skill shots yield a higher score, where when you repeat them the score will be lower).
Here is a score card of the minimum score that you will need for 1 stars on the original 14 echoes:
1- Desert - 2,000
2- Hideout - 2,000
3- Club - 3,000
4- Rooftops - 3,000
5- Marina - 3,000
6- Forbidden Zone - 2,500
7- Park - 3,500
8- Collapsed Building - 2,500
9- Monorail - 3,000
10- Mall - 4,000
11- Downtown - 1,500
12- Storm - 3,000
13- Spaceport - 4,000
14- Jumpship - 4,000
If you are having any trouble check out the 3 star guide:
Solution for Supernova In BulletstormToast gravy has done an incredible job on this and taking even a few of his tips should net you an easy 1 star.