I recently went to the trouble of figuring out how to use BruTile to access ArcGIS online maps. ArcGIS serves the maps as a tileserver. I came up with the following URL to access the tiles of the world topographic map.
Then I used the following code to configure the TileSource
TileSource = new ArcGisTileSource(m_url, new SphericalMercatorInvertedWorldSchema());
The rest of the code to draw the tiles can be found in the examples at the Brutile site. The results are in the screenshot below: