V Sync is the only way to eliminate screen tearing, and only when the frame rate is allowed to match the monitor refresh rate. Whenever they're not in sync the monitor ends up drawing partial frames. Also when possible you should game on a monitor and GPU that supports G-Sync or FreeSync, Regular V-Sync is outdated tech and can cause input lag so is not recommended.
Also not sure why you made this a topic about anti-aliasing,
AA has nothing to do with tearing unless it is causing your frame rate to drop below your monitors configured refresh rate.
And if you use an Nvidia GPU you can try FXAA, because this is the most efficient AA method as you won't lose much performance by doing this.
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