There are a few different types of Boss enemies in Let It Die - the most important being Mid-Bosses and Dons. The Jackals and Forcemen could also be considered bosses, but fighting them is not necessary in order to finish the Story. More information on them can be found on their pages. Most locked gates in front of various escalators are able to be unlocked after killing the Mid-Boss (or Don) in the nearby area. None of these bosses can be skipped, except one of either the 26F COEN or JIN-DIE, and although both must be defeated to access the 27F elevator, you aren't prevented from climbing further regardless.
Both the Mid-Bosses and Dons eventually make a return in Tengoku.
The Mid-Bosses are mass-produced monsters, encountered multiple times by the player as they ascend the Tower. Each new version is stronger than the last, sometimes gaining new moves as well. They are frequently fought by players to farm Faction Metals of the Mid-Bosses's respective faction. However, there is not a Mid-Boss for every type of Faction Metal, so some metals will require different methods to farm.
The Dons each control their own faction, and are the last enemies the player must face before ascending to the next area of the Tower. Their history is told through pages of the Tales From The Barbs magazine, found within the floors of their area. Aside from being able to progress further, defeating them will also give a Large Stamp for the Stamp Rally. There will always be a chest after the fight that has a chance to contain a Faction Metal, though farming the same metals is often easier and faster from the Mid-Bosses.
After defeating the final Don, the player gains access to Battle To The Top, the first post-game area.