This is for picking up random items and opening chests that require you to cleabse them with ether to pick them up.
I found that you needed to cleanse them first, I got lucky on a few runs and the game spawned a lot of ether in order for me to do this pretty fast. It may still count if you do it without cleansing them, but you'll rack up two negative traits that you'll need to get rid of before trying to pick more items up as they'll have a very high chance of being destroyed if you don't.
If you managed to finish this without cleansing, please let me know in the comments so I can edit the solution.
EDIT:
It has been mentioned that you don't need to neccessarilly cleanse these items in order to pick them up to count towards the trophy. However, as stated above you will need to get rid of your negative traits during that run otherwise you cannot pick up new ones, you can return to them and pick them up after doing so.
This tropht can be done in one run if the game allows you to be that lucky.