Well, its either fin rot or this: (hoping for fin rot...)
I'm no expert on treatment tho, but this guy needs to treated ASAP!
Up his water changes to 100% every other day or so... Keeping his water clean will be critical. Wish I could offer more advice!
From the Diseases and Treatments sticky:
Tail rot or fin rot
•Symptoms: Betta’s fins and/or tail seem to be getting shorter and shorter or they seem to be falling apart and dissolving, Black or red along the edge of the betta’s fins/tail, Bloody tips, Behavior may not change
Treatment: Conservative: Treat with Aq.Salt at 1 tsp/gal. Increase water changes to 100% daily. Replace accurate amount of salt following water changes. Add Stress Coat to help repair tissue. If there is little to no improvement within the first 5 days, you can increase the salt dosage gradually to 2tsp/gal but do not continue any salt treatments past 10 days. Medication: If Conservative treatment is ineffective use API Tetracycline, API Fungus Cure, API Triple Sulfa, OR API Erythromycin. Also add Stress Coat to help regrowth. Continue until fins/tail stop receding and start showing some new growth.
Advanced Fin and Tail rot
•Symptoms: Fins and or tail start rotting away, usually starting from the edge, but sometimes it starts at the base of the fin (especially dorsal) and attacks the body directly. Diseases progresses rapidly as the tissues are being eaten away. Once fins have been consumed, rot will proceed onto the body. At this stage the disease is hard to reverse although the betta might continue to live for months if treated properly. If not treated, it will die promptly.
•Treatment: If the rot has advanced onto the body, skip conservative treatment. Do 100% daily water changes. Use a combination of Fungus Eliminator and Tetracycline. Continue until fins/tail stop receding and start showing some new growth. It may take up to 4 weeks to work, so don’t give up.