Before I ever moved into wormholes, I ran level 4 missions in battleships. I had an active armor tank and the mission rats lined up to be killed, and never switched targets. I was not prepared to deal with sleepers.
The first major large difference between fighting Sleepers and mission rats are damage types. In missions, you can look up the damage types of which faction your mission is against and fit accordingly. Sleepers aren't so easy to deal with. They deal "omni" damage, meaning all types. If you have a "resist hole" meaning one of your resists is alot lower than the others, they will exploit this. You can have 80s in all your resists, and 50 in one, then that's what the sleepers will hit you with.
Your ship type is also going to heavily influence your ability to add more DPS over tank, depending on your starting resists. T1 Battlecruisers are going to need to mount some serious resist increasing modules to be able to stick around in Class 2 sites. Base starting resists are why T2 cruisers and T3 cruisers are so much better at survivability in wormholes. They are much easier to fit for more DPS because they already start with good resists which mean less holes to plug. A couple Energized Adaptive Nano Membrane 2s and you're mostly good to go. Plug in a third resist specific module for the harder sites or Class 3s. More DPS also means less incoming DPS because you can whittle down the ships shooting at you faster.
Generally, in the Class 2 hole, looking at it from a perspective of soloing the sites, I would not take lower than 60% in all resists. I'd prefer over 70s in everything. But, depending on your ship, you'll end up with something probably lower than the others, that's just the way it goes. Having 4 in all your resist related skills is very reccomended. Every resist percentage counts.
Another aspect to your tank is your reliance on either an active or passively tanked fit. With an active tank, you are using hardeners that draw on your ships capacitor supply to boost your resists. If you have excellent skills for both capacitor power and in your chosen tanking resist skills, you can certainly make an active tank work. You're probably also in a Tengu or a Legion with those kind of skills. For T2 or T1 ships, passive tank is, imo, the way to go. Why? Because with recent changes to Sleeper AI, Sleepers now use energy neutrailizers. Even with fives in all your energy skills, a single neuting Sleeper BS can drag your cap down to dangerous levels fairly quickly. If you're solo, this can be a death sentence as you wildly try to align to the nearest planet to get away. Throw in a sleeper frig webbing you, and you could be pod-bound very shortly.
Because of this, I rely on a passive tank, which draws no cap to boost my resists, and both, for me, a Damage Control 2 and Medium Armor Repairer 2. Along with a single Imperial Navy EANM II, my resists are 69/60/77/88 for armor. Along with using a "speed tank", which I will discuss in the next paragraph, my PvE Legion can tank entire C2 Radar site spawns and kill them before it is in any danger. Will an Advanced Sleeper BS break this tank? Yes, if it survives for long enough, this tank will fail, both from incoming DPS and because of the Sleeper neuting. When I do Class 3 combat sites, I replace one of my three Heat Sink 2s with a thermic resist module, another with a second EANM 2, and the third with a second Medium Armor Repper 2. Then the only danger to the Legion is losing it's speedtank.
Speed tanking is a form of tanking (increasing the survivability of your ship), that relies on you moving very quickly. This allows you to outrun the explosions of missiles and dodge direct weapons (lasers, hybrids and projectiles) by 'overloading' thier tracking speed, I.E moving so quickly that the turret can't move fast enough to point at you
Read more: http://www.bukisa.com/articles/217446_eve-online-speed-tanking-guide#ixzz1Nsbx1Yex
In essence, speedtanking adds to the amount of incoming DPS you can manage. The faster you can go, without using a MWD, the better your speedtank is. Using this in direct correlation with managing your transversal(you'll have to look that one up, it's got videos all it's own for explanation) allows you to significantly increase your tanking ability by negating some of the incoming damage.
A Zealot with an AB II and good Navigation skills can get up to the mid 500s, while a Legion with the same can do mid 600s on speed.
The speedtank and transversal is what allows solo capsuleers to complete C2-C3 sites alone. The instant loss of the speedtank, through sleeper webbing, puts you in immediate danger and webbing frigates should be killed immediately, except where they are the remaining trigger. Triggering the next wave before you are ready for it can result in the inability to continue the site due to complete tank failure upon warp-in. Example, if you warp into a Sleeper Data Sanctuary, destroy the trigger and do not destroy the three Sirius guns, you will be webbed in place by the frigates and the three sentry guns and the battleship from the second wave will crush your tank.
Which leads to the next suggestion, Download Unknown's Wormhole Tool. Knowing the triggers on the different combat sites is crucial to your ability to take the incoming DPS. You only want to deal with as little DPS as possible if you are solo. If you're in a giant fleet, go ahead and shoot it all.
So, in the end, as long as your ship is:
Resists over 60%
Using a AB to speedtank OR
Using a passive shield regen fit
You should be fine doing Class 2 combat sites solo. If your aim is to do Class 3 and above, you need to increase your tank, as I did by adding more resists and more repair amount, or by adding group mates to deal more DPS. It's quite hard to solo Class 3 sites, but it can be done. The amount of risk it involves is up to you to decide what is acceptable.