Whatever your character is doing isn’t working. Time to change tactics. There’s also a similar phrase–to change tack. But the two words–tack and tactic–are actually not related.
Tacking is what sailors do with sails in order to take advantage of the wind. So when used idiomatically, the phrase means you (or your character) are adjusting to make the most of the situation–e.g. changing your tactics.
Tact can also be a noun, but when used that way, it means to employ skill and delicacy to address a situation. For example: The negotiations required great tact on the part of both representatives.
To sum up–you would either change your tactics or change your tack / change tacks, but you would not change your tact.
On that note, happy sailing! As always, feel free to comment or e-mail me if you have any questions.