In a bowl, whisk together olive oil, lemon juice, parsley, garlic, basil, black pepper, and salt. Pour into a large resealable plastic bag (like a Ziploc freezer bag).
Add in the tilapia filets, seal out excess air in the bag, and press closed.
Move the tilapia around in the bag until they are coated with marinade. Refrigerate for at least an hour.
To make the mango salsa, in another bowl, combine together diced mango, bell pepper, onion, cilantro, jalapeño pepper, lime juice, lemon juice and salt. Toss well. Adjust salt seasoning if necessary. Cover bowl with plastic wrap and refrigerate until ready to serve.
To make tilapia, preheat a large skillet over medium heat. Add just enough olive oil to coat the pan.
Shake off the excess marinade from the tilapia and place them in the pan. Cook for 3-4 minutes on each side, until the fish is no longer translucent and flakes easily with a fork.
Remove from the pan and top with mango salsa.