Turrets are really annoying, since they fire unpredictably. You will need patience and quick reflexes for this (to use double jump or the sword at the right time when needed to avoid being hit). From the early weapons boomerangs can help sometimes (launched while jumping). The frost gun is a marked improvement, since it almost incapacitates the turret, but most useful by far is the flamethrower, as it allows for indirect fire, has massive DPS and is not stopped by walls or obstacles. Finally, it will take quite some time to complete this, as turrets are not as numerous as most other monster types.