The anthropological linguist possess proficiency in linguistic analysis of the sort falling under the umbrella of Basic Linguistic Theory. To put it crudely, s/he can solve problems in phonology, morphology, and syntax.
The anthropological linguist conducts fieldwork in order to collect data in the service of the production of a linguistic description. This has always meant that s/he has an at least decent ear. Nowadays it also implies has some ability to utilize digital audio recording technology and to construct RDBs.