So, I searched about the percentage that appears on the top when the Urgent Quest is available, but I couldn't find out, so I'm asking here.
What does filling the Urgent Quest percentage do? I didn't notice anything different when it reached 100% (most of the time it doesn't reach 100%).
It depends on the Urgent Quest. Most of the time it just means you get a better Clear Bonus Boost, though there are some situations where there are in-Quest things, like in PD getting the ARKS Boost or an RDR boost for the Second Phase of a UQ. In the case of Elder, if 100% isn't reached during the Arms phase, Elder cannot be fought, and in the case of Luther, if 100% isn't hit during the Apple Doritos phase, you end up fighting a "false" version of Luther (though for both, the rate increase is so high that it is almost impossible for 100% to not be reached [in fact, I would be surprised if they took out the part about Elder not showing up if 100% isn't met]).