I have donated mutual fund shares to an eligible charity...does TurboTax handle this or do I have to print and send T1170 to CRA?

Yes, TurboTax takes care of T1170.

When you enter the information under Income > Investments > Capital Gains, there is a field for you to enter the eligible amount of gift.

See attached. 

I entered the full fair value of the shares in the T1170 eligible box, as this is the amount eligible for 0% tax inclusion rate. Turbotax did not reduce my taxable capital gains by the appropriate amount. How do I do it managed the transaction properly before filing my return. At this point it is overstating my table income.