Global shapefile of biomes/ecoregions?
The WWF ecoregions are the original Olsen et al., (2001) classification units. If this is what you are after I would recommend using The Nature Conservancy modification to Olsen that deals with some of the known issues with the original classification.
My preference is the Brown et al., (1998) classification and its Rehfeldt et al., (2012) modification but, it is only available for North America. I would highly recommend against using Bailey's (1983) classification. I have consistently found that incorporating geology into the classification convolves many vegetation and biophysical processes.
There is a relevantly new USGS global ecosystem classification (Sayre et al., 2014) that may be what you are after. The methodology is presented in "A New Map of Global Ecological Land Units — An Ecophysiographic Stratification Approach". The data is available from the USGS Global Ecosystems website.
References
Bailey, R. G. 1983. Delineation of ecosystem regions. Environmental Management 7: 365-373.
Brown, D.E., Reichenbacher, F. and Franson, S.E. (1998). A Classification of North American Biotic Communities. University of Utah Press, Salt Lake City, Utah. 141p.
Olson, D. M., Dinerstein, E., Wikramanayake, E. D., Burgess, N. D., Powell, G. V. N., Underwood, E. C., D'Amico, J. A., Itoua, I., Strand, H. E., Morrison, J. C., Loucks, C. J., Allnutt, T. F., Ricketts, T. H., Kura, Y., Lamoreux, J. F., Wettengel, W. W., Hedao, P., Kassem, K. R. (2001). Terrestrial ecoregions of the world: a new map of life on Earth. Bioscience 51(11):933-938.
Rehfeldt, G.E., N.L. Crookston, C. Sáenz-Romero and E.M. Campbell (2012) North American vegetation model for land-use planning in a changing climate: a solution to large classification problems. Ecological Applications, 22(1):119-141
Sayre, R., J. Dangermond, C. Frye, R. Vaughan, P. Aniello, S. Breyer, D. Cribbs, D. Hopkins, R. Nauman, W. Derrenbacher, D. Wright, C. Brown, C. Convis, J. Smith, L. Benson, D. Paco VanSistine, H. Warner, J. Cress, J. Danielson, S. Hamann, T. Cecere, A. Reddy, D. Burton, A. Grosse, D. True, M. Metzger, J. Hartmann, N. Moosdorf, H. Dürr, M. Paganini, P. DeFourny, O. Arino, S. Maynard, M. Anderson, and P. Comer. (2014). A New Map of Global Ecological Land Units — An Ecophysiographic Stratification Approach. Washington, DC: Association of American Geographers. 46 pages
There was a new map of ecorregions, published as part of this BioScience paper from 2017. https://academic.oup.com/biosci/article-lookup/doi/10.1093/biosci/bix014
Here there is an app to visualiza it, and there is a direct download for the shapefile inside the "about" button. https://ecoregions2017.appspot.com
I would love to read @Jeffrey Evans opinion about it, his previous answer was extraordinarily helpful. In my opinion, it seems a nice updated version, although it does not seem to change much for South America, the region I have looked at in more detail.