You can buy (semi)transparent or translucent shower curtains that already have eyelets in them - at least round my way.

I'd definitely reinforce the holes, Especially if it will be moving around, or getting tugged open / closed regularly.

Maybe fold over a hem and glue it, or tape wrapped round the edge on both sides wherever a hole will be. Ideally you’d have metal or plastic eyelets in plane with the curtain, that the rings then pass through.

If you don't have a hole punch big enough for the eyelets then you might be able to use the eyelets themselves to cut their own holes. Assuming they’re two part metal thingd. put them in place on both sides and apply a clamp or two at the edges of the rings, gradually tighten and see if the rings are sharp enough to cut though, without getting too crushed . if not you could run a scalpel round inside the eyelet.

Of course any glue, tape, cutting method should be tested on some scrap material.

Melting through with a hot poker / soldering iron (even a cigarette) is another possibility, but might be hard to control, and messy / toxic fumes to consider, again a clamped on metal eyelet might set a boundary to the melt.