What almost always needs a license
Any work on the water supply, the drain, or the valve itself needs a licensed plumber in every state covered on this site, both because most jurisdictions require it and because a leak behind a wall is expensive to fix twice.
Waterproofing before tile is the other place where hiring a specialist pays for itself: tile and stone setters bill a median $23.52 an hour, and the hours they spend getting a membrane right the first time are hours you would otherwise pay to redo, since a failure isn't visible until the wall is already closed up.[1]
What a capable homeowner can reasonably do
Demolition of the old tub and surround, once the water is shut off and the valve is capped safely, is within reach for a homeowner comfortable with basic tools. That step is priced at $150 to $300 when a contractor does it, so doing it yourself removes that line from the quote.[2]
Painting, patching drywall outside the shower footprint, and removing old caulk or trim are all reasonable do-it-yourself tasks that don't touch plumbing or the waterproofing envelope.
Where the line gets blurry
Installing a prefab acrylic panel kit is marketed as a do-it-yourself-friendly project by some manufacturers, but it still involves the drain connection and sealing the panels against the wall, both of which need to be done correctly to avoid a leak. A homeowner with real plumbing experience might handle this; most benefit from at least a licensed plumber checking the drain connection.
Setting tile yourself is technically possible but unforgiving: a waterproofing mistake or a poorly sloped floor won't show up as a problem until months later, after the wall is finished and hard to access again.
Where DIY actually saves money
The clearest savings come from demolition, disposal, and any cosmetic finish work outside the shower itself, not from touching plumbing or waterproofing, where a mistake costs more to fix than a professional would have charged in the first place.
If your goal is trimming the $1,500-to-$8,000 national range down, doing the demolition yourself and choosing a prefab kit over custom tile will move the number more than any do-it-yourself plumbing attempt would.[3]
Weighing the trade-off honestly
Every dollar saved by doing a step yourself is also a dollar of warranty coverage you give up on that step. Most contractors won't warranty plumbing or waterproofing they didn't perform, even if the surrounding work is theirs.
If a mistake in a do-it-yourself step causes a leak, the repair often costs more than the original professional labor would have, since it typically means opening finished tile or panels a second time to find and fix the problem.
A useful test before taking on any step yourself: if a mistake there would be hidden behind a finished wall once the job wraps up, lean toward hiring it out. If a mistake would stay visible and fixable, like a paint line or a caulk bead, it's a reasonable place to save the labor cost.