Hello,
Triglycerides are driven not only by fat intake but also
carbohydrates. So in addition to following a low fat/low cholesterol diet(avoid red meat, egg yolks, full-fat dairy, processed baked goods, shrimp, meat sausages, fatty pork etc), try to avoid simple carbs and instead go for more complex carbohydrates in one-serving portions(brown rice, whole wheat bread and pasta, whole grain cereals).