Very simple, my suggestion is that you have the option to show/hide completed achievements from your private achievements list.

This would include the phases that you have completed, without completing the final phase.

The completed phases would just disappear, and leave only the incomplete phase of each achievement showing where the first phase of each currently shows.

I'd then suggest a further option that allows you to hide phases of fully completed achievements. Instead of the phases being listed. It would simply show the achievement name, and 'Final Phase Complete' next to it, in a more streamlined fashion that it is currently.

I should've included this in the original post, but to go even further, the option to completely hide completed achievements (maybe a toggle button) would also be beneficial in my opinion. So Purse Pilferer, for example, would just disappear completely on the 'Hide Completed' list.