There are a few main bosses in Starbound that open up the starmap sectors for further travel into the outer reaches of space. There's a final zone beyond the alpha, beta, gamma and delta sectors known as the 'X' zone, but most of all the tech you'll need to progress throughout the game can be found in the alpha, beta and gamma sectors.
For players who find themselves getting stuck – and it's not hard given that the game is still in Early Access and quests and in-game guides are limited right now – it's pretty easy to get out of the rut by following a few steps to unlock and face down against the main bosses in the game.
Dreadwing The Penguin: Unlocks Beta SectorThis one is pretty easy, as the game's first main quest leads up to unlocking and facing down against the penguin in the flying saucer. You just need to build a distress beacon satellite and activate it to bring the wrath of Dreadwing down upon you. Building the satellite is pretty easy, you just need some silver, iron, copper, wood planks and a few pixel currency.
If you follow the main quest line you should be able to unlock the distress beacon within minutes (assuming you can get your hands on some iron). From there, you signal Dreadwing and when you defeat him you'll unlock the necessary means to travel to the beta sector. The best way to fight him is – if possible – from an NPC village where they'll help you bring down the flying saucer.
Fatal Circuit Robot: Unlocks Gamma SectorNow this boss can be a bit of a pain to unlock. You'll need a series of parts to summon this boss and it can be a pain gaining what you need. First off, you'll need to create an inactive robot. For this, you'll need to make a head, arms, legs and a body. This requires lots and lots and lots of iron. You'll need to temper the iron into steel by using the metalwork station. The hardest part about summoning this boss is gaining an artificial brain. This requires a lot of grind-farming of brains... yes, brains.
You'll need the brain extractor and this requires killing monsters with the brain extractor. Keep killing monsters until you extra a superior brain. There's supposedly a 7% chance to come across the superior brain, so it takes a ton of farming. After you build the inactive robot, defeating it is pretty easy. If you have a sword and shield just block its attacks and attack it during the downtime. Easy peasy. Use the processor to build a robotic crafting table and then make the next starmap upgrade to head to the gamma sector.
The Bone Dragon: Unlocks Delta SectorNow this is a real toughy and not because of what's required to summon the boss but to defeat the boss. Just stock up on titanium ore and fabric. You'll also need 2000 pixels, which you can get pretty easy with an ore refinery; just dump extra ore in for pixels, such as bronze or silver. Use the metalwork station to craft a princess decoy in order to summon the bone dragon.
Now, it might be wise to use a tower or station in which to launch your attack against the dragon. Carve out a small hole where you can pepper the dragon with a gun or other projectile-based weapon. If you try to fight him head-on it's likely he'll burn you into a crisp. Once you defeat him you can craft the next starmap upgrade to unlock the delta sector. This sector contains things like planets made up of tentacles, so be sure to bring plenty of lube or a chastity belt. Good luck and good hunting.
You can learn more about Starbound by paying a visit to the game's official website.