This is Budget if you own the adventure and didn't dust cards from Finley branch...
Mulligan for 1 cost murloc (1/2 or 1/3 is better) and always keep Calling the Finisher and Everyfin is Awesome (but no duplicates). Murloc Tinyfin might help if you have 2 out of 3 mentioned muligan keepers, as it reduces cost for Everyfin if one of your murlocs is cleared.
Calling the Finisher + Everyfin is Awesome in Mulligan can give a quick win on turn 4 or 5 if your murlocs aren't cleared. Play Taunt if it went to turn 4 or later and you don't have murlocs.
Don't draw cards before turn 3, it is a waste of a coin, and overload is way to expensive this early, on turn 2 it is better to Hero Power if nothing else.
Hero Powers from Finley are preffered in this order:
1) Life Tap
4) Dagger Mastery
5) Lesser Heal
if you get the other 3, then it is situational... Armor if you don't have board control, Steady Shot if you about to have lethal only, Reinforce is almost never useful, only if you have not enough murlocs to fill the board and have enough mana for everyfin is awesome and 5-6 minions on board (or that you can put on board)
This can also work in mid-range, after turn 4 keep at least 6-7 murlocs in your hand (Finishers count for 4 of course), try to get Everyfin is Awesome. Against Mage, Priest, Warlock and Shamans, because of the 3-4 health board clears you might want even double Everyfin (unless you are running out of health), but remember for double everyfin you need at least 5 murlocs and 7-9 mana, so be careful with overloads...
If you are running out of health and have only 2 turns as it seems, just play all the murlocs and hope to survive one turn and get a bloodlust, or if you already have bloodlust in hand remember it is only good as last resort or the next turn after Everyfin...