They already tried nuking the rift in the past, but it didn't work then. The only reason why the Marshal gave the order to try once again was because the UN had decided to shut down down the whole Jaeger program. Him giving the order for this mission, just after having lost two jaegers in a battle to defend Hong Kong, was basically one last fuck you to both the Kaiju and the UN ("Today, to the edge of our hope [...] we are cancelling the Apocalypse !").
The only reason why nuking the rift worked this time and not before, was because one of the scientist was insane enough to "drift" (the term used for the memory binding thing Jaeger pilots do) with the brain of a Kaiju, and discovered why it didn't work the first time : the rift, a device created by the aliens on the other side using the kaiju as living weapons against Earth, scan what transit through it, and only let things bearing the "signature" of a kaiju through. As the first bomb didn't bear that signature, it got rejected.
So this time they had a battle against kaijus just around / over the rift, gipsy danger took one in its embrace, dragging it with itself through the rift, and on the other side detonated its own nuclear reactor, closing the rift.
The only reason why nuking the rift worked this time and not before, was because one of the scientist was insane enough to "drift" (the term used for the memory binding thing Jaeger pilots do) with the brain of a Kaiju, and discovered why it didn't work the first time : the rift, a device created by the aliens on the other side using the kaiju as living weapons against Earth, scan what transit through it, and only let things bearing the "signature" of a kaiju through. As the first bomb didn't bear that signature, it got rejected.
So this time they had a battle against kaijus just around / over the rift, gipsy danger took one in its embrace, dragging it with itself through the rift, and on the other side detonated its own nuclear reactor, closing the rift.