As cafeamericano just posted, student visas are issued to those who attend registered universities. Someone once posted that they knew someone who got a student visa because they were taking Tango lessons, but that was probably BS.
I'm not sure if joining a boxing club would make you eligible, but temporary residency can be granted to athletes and artists if you can "prove" that you are one:
Elemento de prueba que acredite su condición de artista o deportista suscripto por la partes. El mismo podrá ser firmado ante escribano público o ante un agente de esta dirección nacional al momento de iniciar la solicitud de residencia.
Google translate:
Element that proves your status as an artist or athlete signed by the parties. The same may be signed before a notary public or before an agent of this national address at the time of initiating the residency application.
So, if you were actually a professional or amateur boxer (with proof of previous fights) and wanted to work with a "professional" trainer in Argentina (assuming there is one), you could give that a try. Joining a fight club probably won't result in a getting a visa.
There are other options:
You might be able to get a temporary resident visa if you are affiliated with a religious institution and are going to do "volunteer" work with that church in Argentina, but that church would have to vouch for you and migraciones might also follow up with spot checks.
SI USTED ES MINISTRO RELIGIOSO, SEMINARISTA O PERSONAL RELIGIOSO CON DEDICACIÓN EXCLUSIVA DEBERA ADJUNTAR:
CARTA DE PRESENTACIÓN DEL REPRESENTANTE HABILITADO DEL CULTO, CERTIFICADA POR LA SECRETARIA DE CULTO, DEPENDIENTE DEL MINISTERIO DE RELACIONES EXTERIORES COMERCIO INTERNACIONAL Y CULTO, EN DONDE SE ESPECIFIQUE LA ACTIVIDAD O FUNCIÓN A DESARROLLAR EN LA REPÚBLICA ARGENTINA, DOMICILIO DONDE SE DESARROLLARÁ LA TAREA Y SI LA ENTIDAD SE HARA CARGO DE SU MANUTENCIÓN Y ALOJAMIENTO.
NOTA: QUEDAN EXIMIDOS DE ABONAR LA TASA MIGRATORIA los miembros del clero secular y los ministros de cultos religiosos reconocidos por la autoridad competente.
Google translate:
IF YOU ARE A RELIGIOUS MINISTER, SEMINARIAN OR RELIGIOUS PERSON WITH EXCLUSIVE DEDICATION YOU SHOULD ATTACH:
LETTER OF PRESENTATION OF THE REPRESENTATIVE ENTITLED OF THE CULT, CERTIFIED BY THE SECRETARY OF WORSHIP, DEPENDENT OF THE MINISTRY OF FOREIGN AFFAIRS INTERNATIONAL TRADE AND WORSHIP, WHERE THE ACTIVITY OR FUNCTION TO BE DEVELOPED IN THE ARGENTINE REPUBLIC IS SPECIFIED, ADDRESS WHERE THE TASK WILL BE DEVELOPED AND THE ENTITY WILL BE CHARGED FOR ITS MAINTENANCE AND ACCOMMODATION.
NOTE: Members of the secular clergy and ministers of religious cults recognized by the competent authority are exempt from payment of the MIGRATORY RATE.
PS: While The LDS church is on the approved list of accepted churches and cults, don't join the Mormon church in hope to be sent on a mission to Argentina. The missionaries have no say in where they are sent.
Temporary residency can also be granted for "special" reasons:
REQUISITOS RAZONES ESPECIALES
Cuando existieren razones de interés público, el MINISTERIO DEL INTERIOR, a través de la DIRECCION NACIONAL DE MIGRACIONES, y el MINISTERIO DE RELACIONES EXTERIORES, COMERCIO INTERNACIONAL Y CULTO podrán dictar resoluciones conjuntas de carácter general que prevean otras categorías de admisión como residentes temporarios.
Google translate:
When there are reasons of public interest, the MINISTRY OF THE INTERIOR, through the NATIONAL DIRECTORATE OF MIGRATION, and the MINISTRY OF FOREIGN AFFAIRS, INTERNATIONAL TRADE AND WORSHIP may issue joint resolutions of a general nature that provide for other categories of admission as temporary residents.
You'll find all the info above (and more) here:
http://www.migraciones.gov.ar/accesible/indexA.php?nomercosur_temporaria
