You need to remove the bumper.
When I've replaced the headlamps/bulbs I also end up removing the front crash bar but I can't remember if that's a necessity or just so I can clean things up. That's just 4 (I think ) M8 or M10 bolts.. so no bother.
The front bumper is supported by a couple of black plastic "ears" under the headlamps and those obscure one of the headlamp bolts or prevent the headlamp lugs from clearing, so those have to come off too... but they're held on with self-tapper bolts.. so all just simple unbolting.
Before fitting new headlamps, since you've gone to a bit of bother and The Darkness is coming.. fit all new bulbs so they'll last all winter and saves you faffing about for a blown bulb a few weeks from now.
And if your "new" headlamps are Used items and/or don't come with the level adjuster motors, I would fit new ones of those too, when you have everything apart. They're an MOT item now and since nobody ever uses them, the reflectors can seize and knacker the motors, or they just die one day and nobody notices. They're not too dear on Fleabay.
Lastly, the headlamps are positioned against the body with two rod "pins" (bolts). This "pin" has a nut/flange half way along it. The idea is this it screws into the car, then the headlamp lug is located against the flange with a nut on the other end of the pin, to hold it in place. It allows minor adjustment, so the headlamp tightens up against something solid.
If your nuts/pins are a bit rusty, so the retaining nut breaks off the end of the pin, then you'll be unable to tighten the headlamp lug up. One of mine died this way, so I had to rig up a regular bolt with nuts/washers on, to replicate the same result.. but it might be easier to buy new ones to have handy before you start.
No. 6 in the diagram .. part number 46800136
Four in total on the car.. Fiat sells them in packs of 5.
Ralf S.