I have a Stellacorn Herder and a Fizz in my base. My opponent casts Bellows Breath with Repeated, targeting both my Fizz and my Stellacorn Herder (including the Repeated). After that, I reveal hidden Tide Turner and move my Stellacorn Herder from my base to the battlefield. When Bellows Breath resolves, can it still affect my Stellacorn Herder, or is it no longer a legal target because it changed zones?

Yes — Bellows Breath can still hit Stellacorn Herder. Moving from base to battlefield is a move within the Board, not a zone change, so the targeting relationship is maintained (FAQ #9062; Rule 359.3.e.3). The "same location" requirement is a targeting-time restriction, not a resolution requirement.

However, since your two targets are now split across locations, the spell's controller picks one location and deals damage only to the original targets still there (Rule 355.11.b; FAQ #7422). So they can deal 1 to Stellacorn at the battlefield, or 1 to Fizz at base — but not both in a single instance. Tideturner, who swapped in, was never a target and takes nothing. Both Repeat instances resolve separately, and each can independently pick the battlefield and hit Stellacorn.

Also note: the swap is a move, so Stellacorn's "When I move, draw 1" still triggers on the chain.