Learn Russian: Орёл, охотящийся над горами, медленно летит к своему гнезду. - The eagle hunting over the mountains is flying slowly towards its nest.

You would write: Орёл, который охотится над горами, медленно летит... To create the present active participle, we take the 3rd-person plural of the verb (охотятся), drop the -тся, and add the participle suffix -щ-, followed by the masculine nominative ending -ий and the reflexive -ся. This gives us охотящийся to match the masculine, nominative subject Орёл.

Why does the reflexive particle -ся appear at the very end of охотящийся, after the adjective ending?

Active participles decline just like adjectives, meaning their case and gender endings change (for example, -ий, -его, -ему). Because the original verb is reflexive (охотиться), the reflexive particle -ся (or -сь) is always tacked onto the very end of the word, completely after the changing adjective ending.

Why are there commas around охотящийся над горами?

In Russian, when a participial phrase (the participle plus its dependent words, like над горами) comes after the noun it modifies (Орёл), it must be set off by commas. If you changed the word order and placed the phrase before the noun (Охотящийся над горами орёл медленно летит...), you would drop the commas.