General synonyms:
* Ascending
* Rising
* Elevating
* Climbing
* Mounting
* Surging
* Gliding
* Floating
More specific synonyms:
* High-flying (for birds)
* Towering (for buildings)
* Majestic (for mountains)
* Exalted (for spirits)
* Skyrocketing (for prices)
Figurative synonyms:
* Reaching great heights
* Achieving success
* Taking flight
* Embracing the unknown
The best synonym for "soaring" will depend on the specific context of the sentence.