I don't think it's just feed any pet. I fed to one pet and than to another and it's not registering the other pet being fed.
feed any pet unique items means they need to be fed to the same pet.
I only have 1 pet. I fed her 8 - r99 foods, and the counter is not registering ~ :( ~
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The wording is definitely ambiguous. I'd change it to "feed a pet...", which is a little clearer and more in line with the descriptions on the other pet achievements.

I fed my pet r99 item of food for the Foodie achievement about an hour ago but it is not showing up she has been fed that one item 0 / 1
The achievement doesn't trigger automatically, you have to go to the 'Food Eaten' page for your pet. It worked fine for me last night.
And I agree with that the wording isn't very good.
~ I wasn't able to get onto the Food Eaten page last night, for some reason the arrow wasn't working. However, it seems to be fine now. Thank you for the reminder ~ ^.^ ~
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Tweaked the wording on this to make it a bit more clear. Is this better, "Feed one pet unique r99 food items!" ?
So this is all fixed if you go to the food eaten page? I have mentioned that the wording is off.
Dexter by ❤
I'm not sure if this is in the same area, but my pet was at 1/10 for Hunger. I fed him 6 R99s and he went to 10/10. Not sure if this is a glitch or if you get more credit for higher rarities, but seems to me he should have been able to have eaten 9 foods.
Formerly known as its_just_me
(I started in March)
Wine is the answer
What was the question?
I don't think that is a glitch. :D
I am going to mark this as resolved. I tested this myself and it awarded the achievement.
Dexter by ❤
I just recently fed my pet (yes, the same pet) about 10 items and browsed through eaten food page several times, and the count is still stuck on 4/5.