It is unknown what Fromund would have thought if he had known that the powerful Elder was moving to the Kirani Colony precisely because Adam was there.
Sure, Bathild would have helped the Kirani Queen in any scenario, otherwise, she would have lost the opportunity to obtain the Twilight Crystal, but Adam was more valuable than that.
By defeating Adam, Bathild would not only fulfill her part of the agreement with the Kirani Queen but also absorb the energy from his body. After he revealed the Path Construct, the fact that it contained two types of energy was a big deal.
But, in addition to the energy, Bathild also wanted to defeat the powerful Phantom.
Despite being an Elder in terms of power level, as she was an Awakened Monster, she still did not have a title.
This did not happen very often, but sometimes it was the case.
Many of Bathild's battles were not well known enough to other monsters for her to be given a title.