-대야 = -다고 해야 = -다고 하다 + -야 (verb ending suffix).
-야 = 1) only if (a stressed condition), 2) even if - a condition to be negated later with contrast effect.
The first sense is similar to -면 (if) but it stress the condition, as in "only if" or "not ... unless". There is also -야만 which is even stronger.
- 잘못했다고 해야(만) 용서받을 수 있어 = You will be forgiven only if you own up to your fault = You won't be forgiven unless you own up to your fault.
The second usage constructs a condition that won't have the intended effect in the end. It's similar to -다고 해도 but is stronger. It's often said with -아/어 보다 (to try).
- 잘해야 / 잘해 봐야 본전이다 = 아무리 잘해도 본전이다 = At best, it's only even (no profit).
- 그렇게 서둘러 봐야 이미 늦었다 = Even if you rush yourself like that, it's already too late.
-대야, -다고 해야 examples.
- 좋대야 좋은 줄 알지 = 좋다고 해야 좋은 줄 알지 = We/They'll only know if you say you like it/them.
- 군대 생활이 어렵대야 / 어렵다고 해야 금방 지나간다 = Tough as it may be, the enlistment period goes by quickly = It might be tough, but it's over in no time).
Other similar forms of contraction involving -다고 하다.
- 한대도 = 한다(고) 해도 = even if they say ...
- 한대서 = 한다(고) 해서 = because they say ...
- 한다는 = 한다(고) 하는 = that they say ...
- 한다면 = 한다(고) 하면 = if they say ...
- 한다지만 = 한다(고) 하지만 = even though they say ...
- 한다기에 = 한다(고) 하기에 = as/because they say ...
* '대' if 하다 conjugates with -여- (하여도, 하여서), and '다' if not (하는, 하면, 하지만, 하기에)