The auction itself is a story element and you cannot miss it. Yet, as LiQing888 pointed out, you can miss out on the bidding itself. Be wary not to choose food instead of the actual bidding :)
There are 3 items on the block in total with a time limit to raise their price.
You can "change" their price by doing small sidequests right before the auction starts, but in total, you need 1000 crowns to buy them all. At this point in the game, you probably have more than that, but I was not sure if my 10K stack is enough. It was :)
If there is a modification if you skip all the side stuff, please let me know in the comments so I can update the solution.
If you are having problems unlocking this chievo and you are doing everything right, Roosta also reports: I also had problems with getting this achievement to unlock on the GOTY edition. After researching online, I found that resetting the Xbox's system cache and doing the achievement again fixed the problem. To reset the system cache, simply go to the Network section in settings. Go to the advanced options and then clear alternative mac address. This should restart the console and then you should be good to go.