I'm still playing this on my PS3 and pet whisperer is the most elusive challenge by far. Most people seem to agree it's bugged, but there's something I've noticed among all the strategies people trying to get it have outlined... no mention of dogs. So my theory is (and I haven't proven it yet, still working on it) that to accomplish the lifetime wish, a sim must train by praising/scolding 10 different traits on cats and 10 different traits on dogs, for a total of 20.
I started with one sim with the pet whisperer wish. I later brought in various cats and dogs during the course of gameplay. Most traits work in pairs, so training one trait on one cat/dog leaves the opposite trait to be trained on another cat/dog. Ideally, your household would have the 1 sim with the lifetime wish, 2 cats, and 2 dogs. I'm not sure if all the pets with all the traits need to be in the household at the same time, or if you can move or age them out, but I'll try to get them all in the household at the same time just to be safe. I suppose starting with 1 sim and 4 pets with the genius trait could be helpful, but I haven't tried that.
Here are some training tactics. Note that I'm only concerned with praising or scolding to gain traits; developing traits by controlling the pet to do actions repeatedly until the trait manifests on its own is not the issue here, as that would not satisfy the pet whisperer wish. Also, controlling the pet to perform an action does not allow the sim to praise or scold that action, so that is not a viable tactic. The pet must initiate the action on its own, or be prompted by another pet or sim, in order for praise/scold to be available. There may be other ways to train the following traits, but these are the easiest ways I've worked out so far.
Friendly/Aggressive: this is probably the easiest trait to train, assuming you control more than one pet. Have one pet socialize with a second pet. The second will usually immediately respond with a socialize of their own (not if they get distracted, such as greeting a sim just coming home). Praise the second pet after they socialize to train friendly, scold to train aggressive.
Neat/Piggy: also a very easy trait to train. Keep an eye on the pet's bladder motive. When it gets low enough, they'll relieve themselves. If this happens outside, praise for neat or scold for piggy. If indoors, praise for piggy or scold for neat. You can speed this up with the epic fail karma power to drop their bladder motive instantly. Use good times to set them right again, then repeat the epic fail as needed.
Destructive/Non-Destructive: another relatively easy trait to train. Keep an eye on the pet's destructive motive. When it gets low enough, they'll scratch/chew on some nearby furniture. Praise for destructive or scold for non-destructive. For cats, they may instead use a scratching post/kitty tower. Use praise for non-destructive or scold for destructive in this case. For dogs, digging will satisfy their destructive motive, so keep your dog from digging if you want to train this.
Adventurous/Skittish: this is only for cats apparently. Cats will sit on some surface-type furniture, like counters or dining tables. Praise this for adventurous or scold for skittish. Cats may also hide under some comfort-type furniture, like sofas, living chairs, or beds. Praise for skittish or scold for adventurous. Sometimes, instead of hiding under, they explore under. In this case, praise for adventurous or scold for skittish.
Playful/Proud: I have only been able to train this for cats so far. Buy a catnip mouse, ball of yarn, or similar cat toy. You can buy a storage box but this is not necessary. With the toy on the floor/ground and the cat and sim nearby, use your sim to nudge the toy. The cat should respond by playing with the toy. Praise for playful or scold for proud. You will likely have to take control of the cat and stop them from carrying the toy away once they finish playing with it, as this can become troublesome if the toy is dropped out of bounds of the lot.
So, at one point, I had my sim and one cat with friendly/neat/non-destructive/adventurous/playful trained, the other cat with aggressive/piggy/destructive/skittish/proud trained, one dog with friendly/neat/non-destructive trained, and the other dog with aggressive/piggy/destructive trained. The pets also had vocal and hunter/digger traits, but these were not trained, they either came with the traits, or developed hunter/digger on their own. That should be 16 traits trained total. I moved out the bad dog, and brought in, one after the other, four more dogs, each trained friendly before being moved out. On the fourth, which should have made for 20 traits total... nothing happened. Hence, my theory above regarding 10 and 10 different traits, and the possible need for all trained pets still in household.
If you are reading this and know of other traits that can be trained via praising/scolding, please post a reply detailing the tactics used to do so. I would imagine that hyper/lazy can be trained, but I have not witnessed pets running around on their own. I'd also imagine that vocal/quiet can be trained, but have not witnessed pets howling along to guitars or stereos on their own, nor dogs barking at stereos or refrigerators on their own. I'd imagine that playful/proud can be trained in dogs, but have not witnessed dogs playing with the rubber ball on their own. I believe some people have found that hunter/digger can be trained by praising, but I have not witnessed pets do this on their own until after already developing the trait. Less likely but also possible, perhaps loyal can be trained in dogs who catch burglars or save sims from fires, but these events are fairly rare so I have yet to attempt this. Also unlikely but perhaps possible, independent/shy could be trained when a pet runs away, but again this is a rare event and I have yet to attempt it.
I know this game likely has very few if any active players any more, but it seems that pet whisperer is the one sticking point for those few of us who still play it. Most people believe it to be bugged, and that may indeed be the case, but if we can determine how to train 4 more traits in dogs, in addition to those I described above, then that might finally make it happen. Good luck, and please post your progress/success.