Surprisingly TACA Peru has a US$ 374 fare from Asuncion to Lima, via (of all places) Montevideo.
http://www.taca.comBus from Ciudad del Este to Asuncion is the easy part, a 200 mile run in less than four hours.
If you have 10 days to get to Lima, you may want to attempt a crossing of the Chaco.
Bus to Asuncion, then another bus from Asuncion to Resistencia in Argentina, then over the bridge to Corrientes across the Paraguay River.
Then a long dusty bus ride across the Chaco to Salta. Daily at 18:00 x 12 to 13 hours. Semi-sleeper.
Here you have an option to carry on up through Bolivia, or cross the Andes to Antofagasta in Chile.
Twice weekly buses to Antofagasta from Salta (via San Pedro de Atacama) departing Tuesdays and Fridays at 07:00 hours x 14 hours.
From Antofagasta there are direct luxury sleeper bus services to Arequipa and Lima.
If you go the Bolivia route, you take the Argentine bus to La Quiaca (Departing at: 5:30 - 10:30 - 15:30 - 22:00 hours), then cross the border on foot to Villazon and pick up a Bolivian bus to Potosi (daily x 12 hours) where you would change buses for La Paz.
If you really want a thrill, take the railway from Villazon to Oruro, Runs four times weekly on Sunday, Monday, Wednesday and Thursday (subject to change). Departs Villazon 3:30 pm.
http://www.boliviahostels.com/howtoget/tren.phpRegular daily buses from Oruro to La Paz,
From La Paz, you can continue to Cuzco via Lake Titicaca. I presume Cuzco and Machu Picchu is in your itinerary.
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