My way:
Boots - left the body out for a night and a day after autopsy. Don't bag it yet, do what you need to until it's past 21:00, then head to your room to send Kim off for the night. Go back to the body, get the boots. You can bag and tag the body the next day.
To get the task in your journal, ask Cuno about the armor, who'll send you to Mañana, where you can express your ambitions to get the whole armor set.
Gloves - once you've gotten the water lock closed, talk to Lilienne's daughter to reveal she hid the gloves in her sandcastle.
Chestplate - also post-waterlock: on the coast, talk to Gary, Morell's partner. Drill him until he hands over the armor.
Helmet - the miss-able one. if you ignored the side quest for the phasmid hunt, you won't get this near the end of the game. So do it all: help Lena find her husband, get pheromone sprayed on you, inspect traps, refill trap, report back, encourage Lena, (not sure if this is required but: get her address!!). Near the end of the game, you'll find the armor after you resolve the phasmid questline.