oh that's easy. You can't.
Complete testing is impossible.
Google "the impossibility of complete testing."
So reframe it not as how do I get complete testing, but what should we do first, second, etc, in the time was have, to do the best possible job?
One way to do this is to code a second program with the same requirments, feed them random input, and look for differences. The differences are bug, or, at least, a different interpertation of the requirements. It is possible both programmers make the same mistake - in which case it looks like a reasonable mistake.
It's likely you won't have budget or time for this, which is good - it tells you the company views testing as an investigation of a certain amount of time/effort to reduce risk, NOT a pursuit fo complete coverage. After that, just test it 'till the time runs out and be transparent about your plans.
