Does revealing Tide Turner and swapping a unit from one battlefield to another make Bellows Breath targeting fizzle?

No, revealing Tideturner and swapping a unit does not make Bellows Breath fizzle.

Bellows Breath targets "up to three units at the same location" — this is a group targeting restriction (Rule 355.11). When its targets move before resolution, the spell does not fizzle. Instead, per Rule 355.11.b and FAQ #9352/#781, the spell's controller chooses a subset of the original targets that are still at the same location, and deals damage to those.

Here's how it plays out:

Tideturner's trigger resolves first (newest chain item). It swaps your unit from Battlefield B with Tideturner from Battlefield A. Your original unit is now at A, and Tideturner is at B.

Bellows Breath then resolves. Its original targets are now at different locations. The Bellows Breath controller picks one location where some original targets are present and deals 1 damage only to those. For example, if Bellows Breath targeted units X, Y, Z at Battlefield B and Tideturner swapped X to A, the controller can deal 1 damage to Y and Z at B (skipping X), or deal 1 damage to X at A (skipping Y and Z) — but cannot split across locations.

If Bellows Breath targeted only that one swapped unit, the spell tracks it to its new location per FAQ #9062 and still deals damage — it does not fizzle.

Either way, the newly arrived Tideturner was never a target of Bellows Breath, so it takes no damage from it.