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.