Assuming "what lies beneath" is decent metal, that damage is quite repairable by a competent auto body man, with the proper tools and knowledge. I personally would not attempt such a job. Large, flat surfaces require a deft touch, a torch to shrink the beaten steel, etc. Looks like a bit of filler was used the last time, and that's a custom lower valence flare, possibly fiberglass.
That's a pretty car you have there; get it fixed correctly. Look for a smaller shop that isn't exclusively devoted to collision repair. If no Fiat owners step up, visit a local Show and Shine event and ask around. You might be able to lower the price by allowing the shop to work on the car in-between other jobs. I'll offer a SWAG of $1000 plus the lamp lenses (hope you don't need a new housing

), plus the red top coat, which is very expensive paint.
Get him some photos of the proper jack mounting bracket. Maybe do the bumpers next year. Not included in my Guess.