Leveling up your ship is accomplished through stat upgrades, allowing a 1-star ship to be upgraded to a 5-star ship over time.
Collect resources by playing DEEPSPACE, then bridge them out and use them to upgrade your ship stats on the blockchain in the Ship Yard. Resources can be obtained in many ways in DEEPSPACE including random discovery events or through NPC interactions and quests (coming soon). A larger amount of resources will be obtained from successfully defeating enemies in combat, or visiting planets and mining for them. You can also buy resources from other places via the Galactic Bank on the DEEPSPACE app.
To upgrade ship stats beyond 50, additional cores are required to improve the power of your ship.
Each additional core unlocks a stat range and unlocks upgrade for all stats.