Who has done it? Do you lose your remote? (is it 1 use?)
Which particular function do you choose from the options to train?
What is the outcome of training besides the achievement?
Quite a few people have done it. You can read about it here: You have been awarded the Universal Trainer Achievement. You pick the USE ON function. And it is one use. The item disappears. As you will also see in the other topic, it is a stat increaser, randomly increasing all of that pet's stats.
I've done it, and yes you do lose the remote after using it. There are MANY things you can do with the remote (it is universal after all) so it can be slightly confusing which options will give you the achievement.
The one you need to select is "Use on Pet" where Pet is the name of the pet you want to train. From what I have seen you can get a bonus of +1-20 to the stats of Level, Strength, Health, Defense, and Intelligence.