This quest uses the Classic Quest Engine.
You may need this map of the Solen Hive
The Ambitious Solen Queen Quest is started by talking to the Ambitious Solen Queen, found in the southeastern part of the Solen Hive and marked AQ on the map. The Ambitious Queen will ask you to do a few tasks
that will help her advance in the Solen hierarchy and eventually become the Matriarch of the Solen. The tasks are relatively simple, the first is to kill 5 of the rivaling Solen Queens, who are also in line to become Matriarch. The second is to collect 50 
Zoogi Fungus, so she can practice transforming it to Powder of Translocation, which is a skill that only the Matriarch masters completely.
To complete the first part of the quest you will need to find one of the two lairs that contain the Queens in question. One is in the northeastern part of the Hive and the other is in the southwestern part, which one you choose doesn’t matter as the spawn is the same in both. Once you find the Queens all you have to do is to kill five of them, note that if you are a friend of the Hive this will most likely cost you that friendship.
While you are killing the Queens you might as well start completing the second part of the quest, which is to collect 50 Zoogi Fungus. Luckily the Queens will have a few of the small mushrooms on them and if those aren’t enough they should be easy to find on the other Solen in the area.
When you have completed both tasks, you should return to talk to the Ambitious Solen Queen again. She will then give you your reward, which consists of a magical 
Bag of Sending, a few units
Powder of Translocation and a few hundred gold pieces.