Yo to fix this problem you either need to one of two things, get rid of the alpha channels on each of the textures that dont need them or use a shader for the model that does proper alpha channels because the engine doesnt render alpha-ed stuff properly.

Heres one that i use:

Give your model this material and it should work fine.

function mtl_alpha_init
{
mtl.skill1 = pixel_for_vec(vector(128,0,0),0,8888); // the first value in the vector is the threshold
}

material mtl_alpha
{
event=mtl_alpha_init;
effect=
"
texture entSkin1;
dword mtlSkill1;

technique vegetation
{
pass p0
{
Texture[0]=<entSkin1>;
ZWriteEnable=True;
AlphaBlendEnable=False;
AlphaTestEnable=True;
AlphaRef=<mtlSkill1>;
AlphaFunc=Greater;
CullMode=None; // CCW or None

ColorArg1[0]=Texture;
ColorOp[0]=Modulate2X;
ColorArg2[0]=Diffuse;
}
}
technique fallback{pass p0{}}
";
}