Though the nature of their existence makes fighting and harming them difficult for conventional fighters, requiring the use of abilities capable of affecting their entire being, as well as the ability to dodge their potentially omnipresent attacks, it is not necessarily impossible, as an omnipresent character's reaction time may still be limited.
This should all be analyzed on a case by case basis - omnipresent characters cannot be automatically assumed to have Infinite or Immeasurable speeds, and attacks coming from them do not necessarily cover the entire universe or multiverse. Some attacks can even be temporally but not spatially omnipresent, and these attacks do not necessarily move through space at Infinite or Immeasurable speeds. Despite the difficulty, it is possible for characters with certain abilities, such as Acausality, Cosmic Awareness, and Dimensional Travel, along with sufficient area of effect or hax, to keep up with omnipresent characters with measurable reaction and attack speeds.