Her true form is most likely a hive mind made of bunch of telepathic microorganisms who take over host's nervous system and marshal the body into production of more Unity, like a virus does to a cell. The yellow puke used in assimilation is most likely Unity in its true form. After assimilation, part of the microorganisms gets into the eyes, turning the normally white sclera yellow.
Once the inhabitants of the planet break Unity's control, they puke her onto the ground and there is a lot of puke. Once enough was puked out, their eyes immediately turn white again.
At one point Rick asks Unity if she can assimilate a giraffe, which means he is not sure, probably thanks to the size of the giraffe or maybe the strength of the giraffe's immune system. I assume that it is about the concentration of the "puke", or microorganisms in the host's body which decides if the host is assimilated or not. Too few and host's immune system is able to fight them off.