Let's get started with some of the first cheating bosses you'll meet. The very first is in a side quest. Meet Treemugger.
This little pugilist has no minions with him. He's a life boss with a unique cheat (until Jamburglar). Wizards will get stunned on the first turn and have their pips reduced to 0. They will have a special no-pip-generation aura that lasts 99 turns. After every turn, all pips wizards have get wiped out and replaced with a set number of pips according to the number of active wizard turns played so far (from the second turn onward). So, on the second turn, wizards will start with 1 pip, on the third turn, 2 pips, on the fourth, 3 pips, etc. Spending these pips doesn't change how many pips you will have on the following turn. After the eighth turn, the wizards will start experiencing power pips.
Here is an elaboration of the fight and cheats for Treemugger on Wiz Central: http://www.wizard101central.com/wiki/Creature:Treemugger
It doesn't appear there is any penalty for latecomer wizards, besides that initial stun.
How I soloed - I planned for a fast big hit while dropping sideboard life shields. He does have pierce, and he does like to Wings of Fate, but slowing up his damage enough allows you to take him out in pretty short order. Three blades and a strong attack may be enough, or you can stack some feints. The good thing about the pip mechanic is heals aren't going to hurt your potential to hit on the next turn should you want to. You can keep casting ever increasing heals without penalty.
The next cheating boss is The Quake Charmer.
He's also got a page on Wizard101 Central: http://www.wizard101central.com/wiki/Creature:The_Quake_Charmer
At the time I started making notes on these bosses, there were no pages up yet, so me adding the cheats here is redundant. But to reduce your click-throughs on my links, the important two cheats are that Quake Charmer frequently free casts Earthquake, and that he will cheat cast a special "bomb" dot that does around 2,000 balance damage when it goes off after the third turn it's on a wizard. It is an AOE dot that does no damage until it expires, and it can be removed via Triage.
Quake Charmer isn't too hard with multiple wizards battling him, but does a good amount of damage for a solo wizard to deal with. Because of his frequent use of Earthquake and tendency to cast big spells, such as Orthrus, Adapt is a very nice aura here. You can opt to spam damage on him, but it is a race against time to hold up against his damage. He can Earthquake two turns in a row, but doesn't do this frequently, so you might try to time your blade casts. Shielding isn't going to do any good, so you can try to stack feints and throw a strong 7 or 8 pip spell on him. Triage in your sideboard can give you an extra turn or 2 of health enough to ensure you can get off your spell. You also still have to deal with his minion so you have to think about how fast you take out Quake Charmer and have enough health to also get his minion.
Next, let's get to the fun little guy known as Jamburglar.
Yes, he's just like that other robble robble guy. He is a shadow school boss, and he has no minions.
It would seem the link for him is only a stub (http://www.wizard101central.com/wiki/Creature:Jamburglar), so let me write out what I know of his cheats.
He has a similar mechanic to Treemugger, but in this case, you start with maximum pips that never get replenished (the Impede spell aura). You are also stunned on the first round. Easy to deal with as a full group of wizards, but as solo, there are some tricky elements to him.
The biggest besides the finite pips for your battle is that he cheat casts a shadow version of Power Nova every turn, and its damage is a percentage of your total health (between 18% and 20%? maybe?). This wound up dealing around a thousand damage to me every turn. It also strikes him! I think this kills universal traps like Feint that may be on him, but I'm not super positive about that. Trial and error. (edit, see below) Being that he's shadow, shielding isn't going to do much good, and on a Reddit forum, I read that he has strong pierce, so resistance gear won't do much good. However, from play, my resist did help me out, so having resist isn't bad. Tower Shields are likely a waste of time unless you go in with super high universal resist. Huh. Just a thought. High resist, Brace to reduce damage, Tower Shield spam... well, the Towers may not work, because I just playtested the fight, and Feint's were not used up on his self-strike from Power Nova.
This is how I beat him solo during my playtest. I went in with various Fireblades and Feints to see if he dispelled the blades (he did not) and if Feints got used on the self-strikes (edit: they were not). I finished with only a hundred health, so be prepared for lots of damage. I had in Fire Dragon, S'More Machine, and Scion of Fire, and threw in a couple Fuel to trigger the Scion. The Fuels and Feints were a mistake, because that took me under the pip threshold to cast Scion. Loading up enough traps to trigger the Scion special critical is a waste of time, as you'll die before you can get your cast off. Double Feint will also take you out of Scion casting, since none of your pips regenerate. Double or even triple Feint is a viable strategy if you are casting an 8 pip spell. Shadow spells, however, are likely not going to save you unless you generate those shadow pips fast. What I eventually wound up with was a regular Feint, a Potent Fuel, as Sharpened Fireblade, a regular Fireblade, and hit with an Epic Fire Dragon. Jamburglar had already take around 4k damage from self-inflicted Power Novas, and my hit did not outright kill him, but he died on the dragon's dot, which is good, because I wouldn't have survived another hit.
There's the first three cheating Karamelle bosses. More to soon follow.