There's a few things you can do to slow Princess down. The big one is to play with the settings. Getting ganged up on? Dial down the Herding, which controls how closely they stay together. This will also enable you to string them out when they have large differences in movement capability, so you can defeat them piecemeal. Getting overwhelmed with units charging into close range? Move the Aggression slider to the left so it engages from a longer range. Tired of it miraculously standing up one-legged Mechs to keep beating on you? Dial down the Self Preservation slider to the right, so it will eject/abandon rather than trying to keep going. This will also have the effect of it conserving ammunition for when it gets better odds. You can also move things around a bit to create a simulated faction behavior e.g. I have a Pirate setting which maximizes damage avoidance (although that setting has minimal effect), maximizes self-preservation (no money to be made on wasting limited ammo supply and not exactly brave enough to stick it out), maximizes engagement range, minimizes herding (they are mostly untrained and barely coordinated), and maximizes pilot risk (undisciplined pilots taking stupid risks).
Tactically Princess has a few holes that can be exploited. There are a few Mechs that it absolutely LOATHES and will chase around the map - Spiders seem to be a favorite, I can usually decoy a whole lance worth of opposition with just one. It also has serious optimization issues with certain designs, just blowing the heat out to nearly shutdown on a frequent basis. The Hellhound/Conjurer is one, as is the Hunchback IIC (ironically, Princess uses this in a very lore-accurate way). When you come across these, just bait it into firing for a couple of rounds then attack in earnest once it is overheating.
If you're using MekHQ to run a campaign/generate OpFor, there's a couple of settings you can twiddle with to make things easier. One of the more important ones controls force type ratios (Campaign Options => Against the Bot tab => Scenarios section => OpFor lance type ratios). Normally this is set to 1-2-3 for Mech-only/mixed/vehicle-only, so that mixed formations are generated twice as often as Mech only, and vehicle only three times as often. With mixed and vehicle only OpFor, the lower BV from vehicles mean you can get seriously (and I mean SERIOUSLY) outnumbered, with 1:3 or worse numbers not uncommon in higher BV deployments. By changing the numbers around, say 4-2-1, you will be fighting against Mechs more often and be only slightly outnumbered. Use weather to your advantage - high winds stymie missile platforms, so if they're fielding more missiles than you are work towards fighting in bad weather.
