The Englisch word »triumphing« in »her triumphing companion« is not an adjective! It is a participle. More precise: It is the present participle of the verb »to triumph«.
Participles live in a realm between verbs and adjectives. In some manner they belong to both worlds, but they are still different from verbs and adjectives. And for this reason participles are often counted as separate kinds of words.
Participles are forms of verbs that behave like adjectives.
And participles do not only exist in English, they also exist in German, and they are not rare. They are used very frequently in German language. In German we have the verb »triumphieren« and the present participle has just 1 letter more at the end: »triumphierend«. So we use the very same construction in German:
Engl: her triumphing companion
Germ: ihr triumphierender Gefährte
Verbs can not be used as attributes of nouns, but adjectives and participles can. And when a word is used as attribute of a noun it has to be declined, this is where the additional ending -er comes from in the example above.
And here is the translation of the complete sentence:
Sie wirbelte herum und sah, wie ihr triumphierender Gefährte aus seinem Versteck auftauchte und in vollem Tempo auf den Hausbaum zukam.
You claimed in your question that the English word »triumphant« (which is a proper adjective) would translate to »triumphierend«. This translation is possible, but it is not the best translation, because »triumphierend« is a participle and describes that the companion is triumphing (it describes that an action is going on), so in German it describes exactly what the Englisch participle »triumphing« means, not what »triumphant« means.
Better translations for »triumphant« are:
- siegestrunken (literal: drunk from victory)
- erfolgreich (successful, high-flying, palmy)
- triumphal (triumphal)