Tamers can't solo peerless bosses or champ bosses, the life leech allows sampires to do that. Cant have that on Tamers. To solo strongest stuff possible for tamer you'll need a nice Greater Dragon or Turtle Dragon and buff it with the consume damage mastery.
You can solo Navrey with tamer, ive done it with my greater dragon but it takes forever. Can solo Bone Demon you summon in doom. You can solo the mini champs in abyss, ive done a few with my dragon. Can solo paragon stuff i guess, ive done paragon balron before and paragon ancient wyrm. Maybe paragon greater dragon with the new consume damage buff. I havent tried stronger stuff with the consume damage yet than what ive listed.
Thing is tamers are great, i love my tamer, they are good all rounders. They can tank things pretty well with GD and Turtle drag. But they simply cant dish out the damage like sampires and other classes can to solo the end bosses. Damage is reasonable but not great compared to other classes so it takes a hell of a long time to solo hard stuff. You can make your damage output awesome with a pet combo like rune beetle/bake or what i personally use is Bane dragon/Tiger or Bane/Bake. But if you do this then those pets aren't tanky at all and you simply cant keep them healed against the tough bosses.
Also being able to vet and greater heal your drag/turtle at same time allows you to heal through alot of damage being dealt to your pet, thats what i do against bone demon etc and with consume damage it makes your pet one hell of a tank, but any monster with Area of effect abilities will quickly switch target onto you or kill you through damage so you cant stand next to your pet and vet it. And most if not all high end bosses have some form of AoE attack or abilitiy that makes them switch to attack you.
Now I just run a pure tamer mage 120 Mage,eval,med,tame,lore,vet. So i cannot speak for how capable hybrid tamer templates are like discord tamer etc.
So to sum up, against the high end bosses you cant get next to your pets to vet them to keep them healed so you wouldnt be able to outheal their damage on your own. And even if you can keep your pet alive it will take forever to kill the boss due to the low damage output.
Tamers work awesome in groups at bosses, having 1 tamer there with dragon to tank boss its great for the team. A team of tamers all healing eachothers pets is capable of taking on almost anything. But if your looking to Solo the big big peerlesses with a tamer, im not sure its possible on your own.
Thats my experience anyway, dunno if someone else wants to chime in.
Edit: I have seen another class that has been used to solo bosses, I read a thread on it a few months back but i can't seem to find it again. It was a Parry Chiv Warrior type template.