It is fine to use "would", but since this is not a hypothetical situation, it is not necessary. Also, idiomatically, tides grow "stronger" and not "higher". Waves (caused by tidal action) might get higher.
There are many ways to say this, but here is one example:
As this star came nearer, the tides on the surface of the Sun grew stronger, and eventually formed mountainous waves. As the star moved away these were torn to pieces and threw off (or ejected) parts into space.
[Edit] I suggested that tides are stronger not higher because tidal action is a force. The resulting waves from tidal action (different from ocean waves caused by wind, but that's a different topic) have an amplitude that can be higher or lower, but the tide itself is measured in degrees of strength and not in degrees of dimension. But this might be overly picky.