Täschhorn (4,491 m) is one of the most difficult 4000er in Wallis group. It's very rarely climbed due to the long and difficult glacier traverse, and easier and slightly higher neighbouring peak Dom.
Ascent: It's highly recommended to sleep overnight at Mischabeljochbiwak. To do the whole tour in one day is very challenging as the glacier traverse is quite tedious. The start point of the tour is Täschalp, there is free parking available. From parking you can take the steep but shorter path to Weingartensee or you can traverse through Täschhütte. From Weingartensee the rest of the path is rather pathless and often difficult to navigate.
The approach to the glacier requires some very good path finding skills and scrambling up to grade 2. There are cairns which you can follow. Once arrive at the glacier, you can stay at the right side of the glacier. Sometimes you have to go through the crevasses on the glacier. Later on the crevasses becomes easy except the last one just before the biwak where you have to jump ;-)
From the biwak, you can follow the ridge to the summit. At the beginning you have cairns to follow and solid rocks to scramble up to grade III. Some sections are exposed, also you have to be careful with brittle unstable rock. Make sure the weather is nice for at least 6-7 hours as it takes long time to reach the summit. Depending on the conditions, there might be snow and ice on the ridge.
Descent: Same as ascent.
Weather: Valley, Summit