0400 - 0600 is probably the second busiest time of day at BOM T2 so leave plenty of time for security and immigration formalities, even with access to the Business Class priority lines. I'd recommend arriving 90 minutes prior to departure to be on the safe side, so 0430 for 0555 departure is about right. The new lounge at BOM is actually quite excellent so its worth spending some time there if you manage to run the gauntlet quicker than expected.
Remember that OLCI boarding passes in India need to be exchanged at the airport counter for "proper" boarding passes, so there is no real benefit to completing OLCI even if you had no checked baggage. Even kiosk check-in boarding passes need to be taken to the check-in counter for a validation stamp.
The flight itself tends to be pretty crap. I've had far and away the worst TK service on this route relative to any other (with the possible exception of Lagos). Expect to be served breakfast immediately after take-off and then nothing else for the rest of the flight. If you request for your breakfast to be held until before arrival, the usual response is that it is not possible so you either eat now or not at all. So plan accordingly. I usually trade away breakfast for sleep and wind up hungry by the time we land in Istanbul - not a major problem as the food options in the lounge are much nicer anyway!