When should we start redemption of air tickets with Krisflyer to ensure higher chances of getting the Business/First Class ticket?

Plan early! Find up the redemption window period and transfer your miles to your KF account a couple of weeks beforehand.

This ensures that your miles are in your KF account during the redemption.

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Transferring of miles from your bank to KF will take a few days, so factor that in as well if your miles are at the bank side and not KF.

However, once the miles are in your KF account, the optimal time to book will be 350 days prior to your intended travel date. So yes, book two one way tickets (to and fro) to ensure that you have the best chances of securing. You'll have to 'camp' twice, but it will be worth it.

If you miss the date or there are no award availability, then consider Star Alliance awards instead, which will still be cheaper than KF Advantage redemptions. And some Star Alliance airlines do give SQ a run for their money.

If that still fails, get on the waitlist and cross your fingers :)