i play Elder Dragon my opponent Tideturner swaps the unit i targetted to a battlefield i already targetted. does this save the unit

Yes — the targeted unit lives. Elder Dragon's play effect is really a stack of separate location-locked instructions ("deal 1 to up to one enemy unit at battlefield A", "…at battlefield B", etc.), and each target is locked to the location it was chosen at. When Tideturner moves that unit to a different battlefield, it no longer satisfies the restriction of the instruction that chose it, so that instruction mistargets and is ignored as the effect resolves (rule 359.3.e.9; see the 2026-04-29 Elder Dragon clarification, which covers exactly this with Flash).

Arriving at a battlefield Elder Dragon also targeted doesn't "re-attach" the damage to it — targets were finalized on the chain, so the instruction for that second location still only applies to the unit it originally chose (that unit still takes its 1). Note this isn't Tideturner redirecting anything (it can't, FAQ #130); the unit is saved purely because the target became illegal.