I only got the game last night, but after reading through some posts here, I tried the suggestions... BINGO first attack on the Sub with Depth Charges and it went down!
Ah, I still remember my first sub kill... Wasted all my Waterbombs (of course), hung around for ages jumping at imaginary periscopes. Nearly ruined my underwear when a big, black thing surfaced in front of me... Then hit the Ahead Flank button