Lately Ive been finding that breeding into a rare isn't as hard as I imagined. For example, I've taken a ...Baku... and set a breeding session with a neighbor with a Dragon. This particular Dragon species was a Chaos Dragon. Even though the percentage for the rare Chaos Dragon was slim, it came out as the result. This has happened for Ragnarok, Vega, Warrior Z, Ornemengar, Proto Zero, and Panda Mew.
When I had the items to affect the probability, I use them. But I've never been able to influence the results more than 10%. So even with that small influence, I was able to get many rare monsters that I would not know where to get otherwise.
On a side note, I guess Panda Mew is considered a rare on some sources, but not in game? In game it isn't stated as rare, just that it is a Mew Pancho combo?