What degree do you need to become an explosives expert?

no "Degree" necessary...

Military E.O.D. (Explosive Ordinance Disposal) are trained "Enlisted" Personnel.

See Film: "The HURT LOCKER"...

These persons require training in military "EOD Technical School"

Detailed background tests... psychological evaluations.... and (possibly the most important) CAN NOT be COLOR BLIND !!!! (CUT the RED WIre..... BOOOM!! --- see what i mean)

In the REAL WORLD ( non-military) it still seems that most explosives experts have had "military training"( after all... the MILITARY is the one who owns things that goes BOOM!)