Unless something is boosting Tidewalker's toughness, when the last time counter is removed, it will be put into the graveyard as a state-based action for having 0 toughness before it can be sacrificed as the result of vanishing.

If you don't control any Islands when Tidewalker enters, its vanishing ability has no effect. (It enters with no time counters on it, so neither of the vanishing triggers can trigger. See "Vanishing" in the General Notes section above.) On the other hand, it will be 0/0 and will be put into its owner's graveyard unless something is boosting its toughness.