First, let's start with the basic setup that is necessary for turning tungsten: ISO K01 (C-4) carbide tools ground with 15° negative back rake and 0° side rake. Use a chlorinated cutting oil. Typical depth of cut of 1 mm (0.040 inches) should use a speed of 27-32 m/min (90-105 sfm) with a feed rate of 0.18 mm/rev (0.007 inches/rev). The tool should have a large lead angle (side cutting edge angle) of ~ 45°.
Now, is the crumbling occurring when you machine to an external corner? If so, use a support made out of a machinable thermoplastic material such as nylon. Also, use a large chamfer that is machined before the adjacent surface is machined. This chamfer should be sufficiently sized such that there is some metal still left after the turning cut is complete.
source: ASM HANDBOOK Volume 16 Machining
If you don't have this reference, then you really need to purchase it, especially when machining difficult materials like tungsten.