A BNA TRACON Controller reported when an unidentified VFR aircraft flew across the final approach course they had to vector two air carriers off of their approach to avoid the traffic. The VFR aircraft began a descent resulting in a NMAC with one of the air carriers.

Narrative

Non-participating; non-ADSB; 1200 VFR code was observed violating the class C airspace at 3500 ft. The aircraft proceeded towards the final approach course for Runway 20L where 6 aircraft were being sequenced onto final. The nonparticipating aircraft appeared to remain at 3500 ft. so I descended all aircraft into BNA to 2500 ft. in order to go underneath the VFR traffic that was heading towards a 12 mile final. Aircraft X was on a 12 mile final when that VFR traffic was overflying northwest bound and starting to descend. I called traffic and Aircraft X had the traffic in sight. I then called traffic to the preceding Aircraft Y and told them to expedite their descent to 2500 ft. At that time the VFR target started descending quickly and turning directly up the final Runway 20L head on to Aircraft Y.I then issued a traffic alert; probably the best one you will ever hear in your life; told Aircraft Y to stop descent and turn heading 110 immediately. I did not cancel their approach clearance because I felt the traffic alert and avoiding a head on collision in 10 second was slightly more important. I then told the preceding traffic to Aircraft Y; Aircraft Z to turn and stop their descent to avoid the VFR traffic and keep the sequence. No RAs and no deaths reported. Expand the Class C and start working on finding the non-ADSB aircraft that violated the Class C. Although the aircraft violated the Class C; the almost near midair occurred outside the class C.