Grinding noise from rear when accelerating (with videos)

i doubt this will find the problem, but did you check under the car to make sure there's no debris stuck stuck around the drive shaft? I got a small stuck up there once that made a similar sound, only at certain speed/rpms. I doubt that's whats going on here, but its an easy check.

how fast are you losing AYC fluid? If you have to top it off more than once per year, then that's your problem. Any signs of leaks underneath?

Looks like you'll need the diff replaced or rebuilt. Is the car modded? If not, make mitsu replace it. If so, talk to IAG.

have you had the rear diff fluids serviced? if so, who serviced it? when? some others had shops totally fuck up their rear diff and AYC when screwing up the fluid flush.

Did you buy it from a Mitsu dealership? Did they include a warranty? If so, then you're good. Otherwise, if the warranty was voided, then you're screwed.