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Distinguish Datasets by Using Legends
Use a legend to distinguish multiple datasets.
In[1]:=

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data = GatherBy[Table[

    {CountryData[c, "Continent"], 

     Tooltip[CountryData[c, #] & /@ {"BirthRateFraction", 

        "DeathRateFraction", "Population"}, CountryData[c, "Name"]]}

    , {c, CountryData[]}], First];
In[2]:=

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legended = MapIndexed[

   Legended[

     Style[#[[All, 2]], 

      ColorData["Rainbow", (First[#2] - 1)/(Length[data] - 1)]],

     #[[1, 1]]] &,

   data

   ];
In[3]:=

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BubbleChart[legended]
Out[3]=