Breakthrough: Peak Shard and Max Job Level

Peak Shard is an item that you need in order to increase your Max Job Level after Breakthrough. 

You will need 9 Peak Shards in order to increase your Max Job Level by 3. 
You can get Peak Shards from this NPC inside your Guild Territory. If you don't have the NPC, you may need to talk to your Guild Leader about it.

Once you have 9 Peak Shard, go to this Alice Fona NPC inside Guild Territory.

She will increase your Max Job Level by 3

Also, Assistant achievement would also give you some.

Personal Suggestion:

• Start Getting Peak Shards even before getting Breakthrough since you can only get a limited amount per day.
• Upon research, you don't need to continue hoarding Peak Shards once you reached Job Level 70. You can use your Silver Medals for other stuff instead.