Sometimes when you are down to heads up, you need to play chicken more than count on cards. By that point in the tournament, you should know what kind of betting your opponent will call and what kinds he will fold to. Some people can see through all-in betting. Some people are more weary of pot sized betting. Some people think that value bets are the suspicious.
You need to find out what the betting pattern is the most fearsome to your opponent.
So you are in fact, when in first aggressor position, going to play chicken and not cards.