Blast Shards are radioactive pieces from the epicenter of the explosion that started all this. Collecting Blast Shards gives you new Battery Cores, increasing your energy meter. Blast Shards are given as rewards for some side missions, and are also scattered around the game world. You can search for Blast Shards by pressing 
for a radar pulse. Blast Shards show up as dark blue circles on your mini-map. There are 350 Blast Shards scattered around the map; plus the ones you earn for completing certain missions.
Here is a list of how many Shards you need to collect to get a new Battery Core:
- 5 Shards
- 15 Shards
- 20 Shards
- 30 Shards
- 30 Shards
- 35 Shards
- 35 Shards
- 40 Shards...
Each new battery core is gained with 40 more Shards. There are 350 Shards scattered around Empire City, and more are available during certain side missions. However, you can only have a maximum of 24 battery cores.
Hunting for Blast Shards is tedious; and, you don't really need a huge number of extra Battery Cores to beat the game; so, only go after them all if you want the trophy. The best way to hunt Shards is to make a perimeter run around each island; then, go over the rest of the island block-by-block. There are a couple of Shards most people miss. One is way out on a broken pier on the east side of the Neon. The other is on top of the ruined skyscraper next to the blast site. These two Shards are far enough (laterally and vertically) that they don't show on your radar.