in most states, exterior work is the province of the condo assoc,,, we do a fair amount of condo work but NEVER for the individual unit owner - ONLY for the condo assoc.
repair method's fairly simple - 1, delineate the size of the damaged conc which will often be much larger than your broken piece; 2, sawcut the outline of the patch; 3,chip off the bad conc to find good; 4, scarify the existing conc to provide a good mechanical 'tooth' for your selected repair mortar; 5, select the right repair mtl & apply if properly; 6, cure per directions.
ps - be sure you've got rebar in the right space,,, tie it to the existing bar OR install it per icri specs,,, we like epoxy coated bar for balcony work.
pps - be sure your insurance will protect you in case any falling debris injures anyone OR damages any property.
pps - this will likely be permitted work meaning stamped engineering/architectural drawings.
ppps - you may also be required to be compliant w/ALL osha specs AND post a performance bond.
you absolutely sure you want to do this on your own ? it may be your ceiling BUT the responsibility for the repair is on the upstairs owner according to most laws,,, its HIS deck, not yours :yes: