To fight Queen Slime you must find Gelatin Crystal in the Underground Hallow. It grows on walls similar to crystals. You can then summon the boss on the surface.
To fight Empress you must kill Prismatic Lacewing critter in the Hallow. It only spawns at night, but you can catch it and then release during day. Fighting and killing Empress at day rewards you with unique Terraprisma weapon... but you'll have to dodge every single attack or use the strongest weapons to quickly kill her.
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