Großer Krottenkopf (2656 m) is the highest mountain in the Allgäu Alps of Austria. The easiest route is a normal hike with a bit of climbing (UIAA I) briefly before the summit. I would choose the overall difficulty of the route to be T4(I). It's not a bad idea to split the hike in two days and sleep in Hermann-von-Barth-Hütte.
Ascent: Starting from Elbigenalp parking lot, follow the signs towards Gibler Alm (20 minutes), the path is short but not so steep through forest. From Gibler Alm follow the signs towards Bernhardseck, 30 minutes from Gibler Alm according to the signs. After that the path goes on the ridge offering amazing views of Allgäu Alps all around. The ridges goes through Mutte all the way to Gumpensattel. In the last part, you might encounter some snowfields and traversing through steep gravel. Surefootedness is required in this section. From there follow the signs towards Krottenkopf (track 437). There are some steep rocky sections with rope in the traverse. The last section to Krottenkopfscharte is steep and rocky. From there the summit is 45 min. The last part to the summit is T4 and requires scrambling upto UIAA I.
Descent: Follow the same path as ascent to Krottenkopfscharte. Then follow the signs towards Hermann-von-Barth-Hütte. The traverse is long and often going up and down. From Hermann-von-Barth-Hütte, follow the signs towards Elbigenalp.
Weather: https://www.wetter.com/oesterreich/elbigenalp/ATAT30118.html