How does the terrorist assemble amd transport it?

Nuclear bombs using Pu239 are hard enough to handle, even though the half-life is some 25,000 years. The stuff continuously gives off Gamma rays that will penetrate damn near any shielding. Significant quantities of Pu239 are also noticably warm to the touch because of radiogenic heat.

An intensely radioactive isotope is shot-lived. The more intense, the shorter the half-life. Even non-penetrating Alpha rays generate very penetrating X-rays when stopped by neuclei. Beta rays also generate penetrating X-rays. These penetrating radiations will escape (in some quantities) from any shielding whatsoever. Gram quantities will spontaneously melt their way out of any container in short order, unless a coolant flow is provided.

The basic unit used to describe the intensity of radioactivity in a sample of material. The curie is equal to 37 billion (3.7X1010) disintegrations per second, which is approximately the activity of 1 gram of radium.

By the time you have both (1) enough radioisotope to make a bomb a serious hazard, and (2) enough radiation shielding to make the bomb transportable, you are talking about a massive thing. Add enough explosive to burst out from the shielding, and it is still more massive. Even tiny samples use many kilograms of shielding. Large quantities would require hundreds of kilograms of shielding just to permit the terrorists to survive transporting it, even if they wanted to "martyr" themselves and die by radiation poisoning. To scatter the bomb contents thoroughly, hundreds of kilograms of explosive would be required.

Furthermore, the leaking radiation, and there is always some, would make detection of this device rather easy.

The terrorists would get more damage for the buck by using toxic chemicals. These are much easier to handle than radioisotopes.

One should note that no nuclear nation has ever designed a "dirty bomb" for military use. There are very good reasons for this.