Trying to get the tuxedo medal

You aren't doing anything wrong. It's a problem that the game has been having. Apparently, LOTS of people are having this same problem! And I'm one of them!

To get the penguin you have to stay an entire week in the house petting your penguin just keep your sim alive

I have been haunted by this medal for a very long time, since I bought the game in middle school. I once came very close to completing the game (99%) but was unable to because of this last medal.

A couple of thoughts occurred to me this most recent time I picked the game up to try to get Tuxedo again. I had never tried to survive a week with ONLY the Unsinkable Treasures penguin in my house, and I had never tried to obtain it before getting a cat or dog in the game. The game never specifies any details about obtaining the medal, so I thought maybe there was an "only" missing from the description.

The thing is, I know for a fact one other errand or medal in the game is glitched. I don't remember if it's a medal or an errand, but you're asked to sell 99 recyclables, but it only works if you've not sold any while you're playing the game, or some other strange thing. The penguin raises your pet affinity skill level, which means that it counts as a pet. Therefore, perhaps having a cat or dog locks you out of getting it.

I tried staying in my house for a week, with only the penguin as a pet, NO cat or dog, and I was finally awarded the medal.

I have not tested this any further, for instance, I don't know if selling your cat or dog makes this able to be unlocked, or if ever owning another pet makes it unable to be obtained. I'm unsure if not being awarded the medal is a glitch or a hidden stipulation, but those are the conditions under which I was able to obtain it.

This game is old and kind of an odd one to come back to unless you have any nostalgia for it, so I suspect this answer to a nine year old question won't be very helpful to anyone. However, I wanted to put a more in depth answer out there anyway, as other answers to this question have been fairly unhelpful to me, the number of times I've searched this (lol).