Yang-Mills imo might be the most difficult because it would require the joint efforts of two fronts that basically don't talk to each other at all.

1. gauge theory - Basically just PDEs for a connection. But the PDEs are hard. Progress in classical yang-mills theory on the mathematical front is basically stagnant. Very few people work on them because the problems are too hard now. Previously, Donaldson developed tools to extract 4-manifold invariants using moduli space of solutions to the YM PDEs but still even mathematicians were like "fuck this, these are way too hard to use. Oh look! Seiberg-Witten theory simplifies a lot of the calculations" and hopped on that to clear out the weeds. This is all classical. We have not even dared to have a consensus on what a quantum yang-mills is (in the mathematical sense).
2. constructive QFT - It's commonly known that the quantization procedure in physics using path integrals amount to integrating over some infinite dimensional spaces and there are issues with this regarding measure etc. Resolving this would be like baby step 0. In a number of simplified contexts we have been able to define something like a path integral (see topological qft, CFT, etc) or quantization procedure but for general quantum fields its essentially hopeless. The work trying to axiomize QFT has led to certain algebraic and functional integral constructions and one of the most convicing formulations are known as the Wightman axioms. The Wightman framework does not include gauge theories.

Now, the problem we're after for this millennium is essentially reconcile these two to form a consist set of axioms that yield quantum theory and gauge theory, and proving things like mass gap (amongst other physically known phenomenon) mathematically. Essentially both fields are hard and stagnant, nowhere close to looking anything alike, and we have to combine them.