I assume when you say Chile you mean Santiago.
The easiest but not the shortest is a bus from Santiago to Mendoza (6 hrs) and a connecting bus from Mendoza to Buenos Aires (overnight), which you can buy all at once in Santiago. Then Buenos Aires to Asuncion (18 hrs).聽 If you feel like a bit of masochism, don't miss your connection in Mendoza because of the usual holdup at the border with Argentinia, and have your Paraguayan visa you could arrive in BsAs in the morning and then leave to Asuncion about 3pm the same day when most of the buses leave. Catch the earliest bus out of Santiago to maximise your chances.
The shortest would involve a bus from Mendoza through Cordoba to Resistancia, then a change to another bus to Asuncion.聽 I have no idea how long this trip would take.
If you are in the far north of Chile you can take a bus directly to Salta in Argentina.聽 You then catch another bus to Resistancia then change for Asuncion.
If you are in the south of Chile, take any bus that goes to any town in Argentina then catch a bus to Buenos Aires, than as above to Asuncion.
Chilean, Argentinian and Paraguayan International buses are great; comfortable, safe, cheap and run just about everywhere.
