Black is alive, there is no way to kill.
Discussion follows.
W plays 1 in diagram 1 and gets a ko.
White 1 and 3 are tesuji. Black 2 in Diagram 1 is not the best answer. Black 4 left of 3 does not work either.
Instead, B plays 2 Diagram 2...
..and still cannot live unconditionally...
... but gets either the ko here...
...or this ko, which is probably the best way to play for both.
Pok
unkx80: I disagree with this solution. Black plays , and lives because a and b are miai.
Tderz: Food for discussion:
look closer at the relation of the inter-acting white key points a, b and c. What is their right order?