After you complete The Gilded Cage in Chapter 4, you'll be able to visit Algernon at his place in the northern outskirts of Saint Denis. Upon speaking to him, you'll learn that he wants you to head out into the world and gather exotic plants and other animal parts for him. This is arguably the longest Stranger Mission in the game and it's a good idea to accept it early and work on it as you progress through the game. The Interactive Map will show you where you can find everything but below you'll find a short summary of where to find each plant per step.
Duchesses and Other Animals II
|5 Little Egret Plumes||Bayou Nwa||Use the Varmint Rifle|
|5 Reddish Egret Plumes||Bayou Nwa||Use the Varmint Rifle|
|5 Snowy Egret Plumes||Bayou Nwa||Use the Varmint Rifle|
|15 Lady of the Night Orchids||West of Bayou Nwa||Begin your search around the "B" of Bayou|
Your reward for this step is $110 once you return to Algernon and he'll hand over another list.
Duchesses and Other Animals III
|20 Heron Plumes||Northern Bayou Nwa||Use the Varmint Rifle|
|7 Lady Slipper Orchid||West of Big Valley||Begin your search above and below the "B" of Big Valley|
|10 Moccasin Orchid||Southeast of Elysian Pool||Begin your search to the south of the "R" of Hanover|
Return to Algernon and receive $125 followed by the list for the next set of items.
Duchesses and Other Animals IV
|25 Gator Eggs||Bayou Nwa||Search around the swamp for Gator nests|
|3 Acuna's Star Orchid||East of Lagras||Search the land to the east of Lagras or around Lagras itself|
|7 Cigar Orchid||Bayou Nwa||Search to the west and south of the "N" of Nwa|
|5 Ghost Orchid||Islands southwest of Saint Denis||You'll find a group of islands to the southwest of Saint Denis where these will spawn|
Once again, return to Algernon to receive $150 and obtain the list for the next set of items.
Duchesses and Other Animals V
|30 Spoonbill Plumes||Bayou Nwa||Use the Varmint Rifle|
|10 Rat Tail Orchid||South of Lagras||Begin your search around the "N" and "W" of Nwa|
|5 Spider Orchid||West of Bayou Nwa||Begin your search around the bending river to the west of the swamp|
|5 Night Scented Orchid||Southeast of Braithwaite Manor||Begin your search around the meadows to the southeast of the Manor on the map|
Return to Algernon once again to deliver the goods and receive $175 along with the final list of items.
Duchesses and Other Animals VI
|5 Clamshell Orchids||Islands southwest of Saint Denis||East of Caliga Hall and Southwest of Saint Denis|
|5 Dragon's Mouth Orchids||Grizzlies East||Search around the lake of O'Creagh's Run|
|5 Queen's Orchids||Lakay||Search between the south of the letters "L" and "A" of Lakay|
|10 Sparrow's Egg Orchids||Annesburg||Search around the fields of Annesburg|
When you deliver the final set of items, you'll obtain $200, an Exotic Hat and Algernon's Revolver along with completing the mission.