Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.

Mash potatoes with a ricer or hand mixer until smooth. Gradually stir in oil until potatoes come together; add aji amarillo, salt, and pepper. Cool potato mixture in the refrigerator, about 20 minutes.

Stir tuna, onion, and 1/4 cup mayonnaise together in a bowl.

Line a casserole dish with plastic wrap. Spread 1/2 the potato mixture on the bottom of the dish. Spread 2 tablespoons mayonnaise over the potatoes, spread the tuna mixture over the mayonnaise, and place the avocado slices in a single layer on top of the tuna mixture. Spread the remaining 1/2 of potato mixture over the avocados, and top with remaining 2 tablespoons mayonnaise. Place sliced eggs over the top. Cover casserole dish with plastic wrap and refrigerate until firm, about 30 minutes.

Invert casserole dish onto a serving dish or baking sheet to remove potato casserole from dish. Remove plastic wrap and cut casserole into squares.