Just like the other shrine achievement, this is completely luck based. You also must pass the same shrine 4 times in a row. Passing one shrine 3 times, then passing a different shrine will not unlock the achievement. As far as I'm aware, there is no way to increase your odds.
According to SinFluxx, it seems possible to unlock the achievement using multiple shrines if you use the shrine until it's destroyed. Please see his comment below!