"The Terrible Experiment" Mythos Card - How to deal with it?
The first time we encountered this rumor, we used Flute of the Elder Gods on it.  On reread, I suspect we were cheating but if you don't agree then that might be a strategy...which could be generalized as try and buy stuff to help (you do have a couple turns to prepare right after the rumor appears).
Note, the rumor also says &quot;one or more monsters&quot;.  In subsequent runs I've definitely cherry picked the easy ones and let it build up again.  This is somewhat luck based and won't help you if they're all harder than you can defeat.  Similar to the above comments and other answer, if you have no-one who can fight at all, it is probably better to push on, so is dependant on the variables of the game (which make the game replay value skyrocket IMO=)).
I guess along with the above strategy if you have a bunch of easy monsters as trophies might be worth spending them to get them back in the pool.
It may also be noteworthy to newer players that the positioning of this rumor is between Hospital and Asylum so if you have a lot of money isn't a terrible position to recharge in between fights (well one stat anyway).  This is dependant upon how clean your streets are/your sneak, another variable :D
Really this answer and likely any answer could be applied to fighting in general.  The rumor just adds a terrible downside if you fail.