Bring a large pot of water up to a boil for the pasta. Heat olive oil in a large skillet over medium high heat. Season the barramundi with salt and pepper, then place them in the pan and cook until opaque throughout, and lightly golden on all sides. Use a slotted spatula to gently remove the fish from the pan, and set aside.
When the water is at a rolling boil, season it with enough salt to make it taste like the ocean. Drop in the pasta and stir, then follow package directions to cook until al dente.
Add the garlic to the remaining oil in the pan and cook until just starting to turn golden, about 1 minute. Add the tomatoes, juice and all, and use a wooden spoon to break them apart into smaller pieces. Simmer, uncovered, on low heat for about 10 minutes.
Drain the pasta and transfer it right to the pan with the sauce. Add in the capers and barramundi and toss to coat, adding in some reserved pasta water to thin it out as needed. Add half of the basil leaves and almonds, then toss until fully combined.
Transfer pasta to a serving dish. Drizzle with a little bit of olive oil and top with the remaining basil and almonds. Serve immediately.