I would start with J2, which forces a white response around K3 (otherwise w loses the G4 stones). White cannot respond at H2 because of J4. If w connects at K3 I would connect at H2. Now, the lower black stones have 5 liberties which seems favorable with respect to the white E3 group. Side variation: If w replies at K2 instead of K3, J4 does not kill G4 (self atari at K3 ;-) ), however b gets H2 in sente and can play F2 afterwards - again 5 liberties - and the keft w stones will die.

Or is black supposed to kill all of the w stones? That would come quite as a surprise for me... :scratch:

Edit: Starting right away with F2 - E2 - E4 may look tempting, but w can stretch to E1. In the following semeai b can only get the single C2 stone but not more. Thus, b needs to gain an additional liberty first.

Just for reference: Here is the main line from the answer. The - -exchange seems to make sure White cannot push through at after . Though, I think with capturing six White stones, White's position will surely collapse.
Anyway, I think pushing in at first is better style since when White does not answer at , you don't need to kill Ko-threats with and so on.

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . X X . . . . . . . . . |
$$ | . . . X . . X X O O X . . . . X . . . |
$$ | . . . . . X O O O X O O O O . . . . . |
$$ | . . X X . X O 4 3 X . . X . . X . . . |
$$ | . . X O O O X O O 6 O O X . X . . . . |
$$ | . X O . 2 1 X 7 5 . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]

It's White's turn again and he can still try something wicked : D