There are two parts of the champ: the spawn and the champion.
You can work out most of the spawns (but for sleeping dragon, the two in abyss and maybe twisted glade) but the only champion you can solo as a tamer without going completely mad is barracoon (ratmen).
Mephitis (spiders) is probably the worst.
For the undeads just try not to get too many spellcasters on your greater dragon (as we lizardmen say: take the dog if you want to play fresbee): note that to advance the spawn you don't need to engage ten mobs at the same time, you just have to keep killing and the undeads go down very fast if you take them one per time. Also try to not get caught in the middle of the battle field when the spawn goes to the next level because with lichs death is granted if you're on feet.
Wear a suite with good resistances and a mage weapon if you can, don't be afraid of jumping in the gang to use bandages on your scaled friend and hide a lot.