Across the Ahuriri valley from Top Hut is an impressive wall of waterfalls. The route described here traverses lower-angle tussock slopes above the waterfalls, from left to right (south to north). But first there is some route-finding and exertion to get up to those lower-angle slopes.... Credit to Dave Crouchley of DoC on our trip, for suggesting the route up to the tarn, after scrutinising the topo map while we were camped at Top Hut.
1) At the northern edge of a grass-covered boulder fan, climb to the left through bush that is initially open then scrubby and very steep (including rubbly rock). On this face, the scrub ends below some bluffs. Now in tussock, sidle to the right up onto the spur. The route marked on this site's route map for the section described above is only approximate.
Climb the spur until you can see a descent into the first creek to the north. You may end up going higher than you really need to. The terrain is short tussock and slaty rock covered in gravel. Descend (or maybe sidle) to the creek.
2) Alternatively from the Ahuriri climb the bush spur on the downriver side of the grassy fan to reach the terraces above (as shown on map). Climb the now-grassy spur towards bluffs above, swinging left into the start of the large hanging valley. A small tussock gully will become visible just west of the spur, climbing north to get you back onto the spur above the bluffs. Sidle / climb north either dropping into the head of the large basin or sidling scree above it.
Once on the tussock/scree there is no need to cross any dangerous ground - just keep looking for the best route.
Make a long ascending sidle northwards, onto the NE ridge of peak 2230m, climbing a steep scree face to the ridge at the first reasonable-looking place you can find. This is the second scree chute shown on maps to the south of the main banana-tarn valley, hitting the ridgeline at the 1900m contour. The last part of the ascent to 1900m may be snow-covered in summer and is steeper, as the contours show. Ice axe and crfampons were a must in early January.
From the shoulder of the ridge at 1900m described above, sidle west on rocky scree and snow patches to the small spur which falls northwards to the outlet of the big tarn, This spur is steepish rock and is bluffy on the west, so stay away from the left on the way down. Cross the outlet of the tarn and find a way around the tarn then climb (probably snow most summers) to the pass at 1990m. We found the tarn partly ice-covered in December and went around the northern shore of it.
Since we went there, the route has has been included in Moirs Guide and also informally named Banana Tarn Pass (the tarn might look this shape in some summers, depending on the ice/snow cover).
From the pass descend scree and tussock west to the bushline at the stream forks shown on the route map. Sidle scrubby bush westwards onto the spur and descend the crest of the spur all the way to the Hunter River. When we were there in 1985 it was very heavily browsed by deer and the bush looked nearly dead, so I hope it has recovered in the years since.