This Riven Challenge is easy to do with any Warframe you like - just make sure you equip some mods that will increase your Loot Radar range e.g. Thief's Wit, Animal Instinct, Primed Animal Instinct etc. - this will allow you to see containers with loot as white rectangles on the mini map and will also show Syndicate medallions (and Ayatan treasures and caches) as white rectangles.
Start a Syndicate mission in Solo mode and use your mini map to check every loot container on the map. If you are not familiar with the map I recommend that you break the containers and loot the items - this will make the container disappear from your mini map so you don't risk running and checking the same spot twice. After you have run a specific map a few times you start to get an idea where the Syndicate medallions may spawn. Also notice that Syndicate medallions often spawn at the same locations as Ayatan treasures so try to remember those spawn locations. After a while you learn which rooms are likely spawn locations and which you can just skip.
The easy way to find those Syndicate medallions (and Ayatan treasures) is to use a Warframe with an ability that can break all nearby containers, which will save you some time. Limbo modded for Range and Efficiency can spam his Cataclysm ability in order to break all nearby containers - see my "CataBomb" build below for an example. On low level missions the Cataclysm will also kill nearby enemies so you don't have to waste time fighting them. Use the Vacuum or Fetch mod on your companion to have them assist in picking up any loot from the broken containers, then check your map - if there is still nearby white rectangles on your map it might be a Syndicate medallion - go check it out!
This build focus on maximizing the range of Limbo's Cataclysm ability and be able to spam it over and over. Notice there are no Health/Shield/Armor mods in this build so it is not recommended to use against high level enemies!
When running around searching for Syndicate medallions I prefer to open the large overlay map (press-and-hold the M button) which gives you a better overview of where there are nearby containers to check out. As you get close press the #4 Cataclysm ability, run near the loot to pick it up and check your map - if there are still nearby white rectangles on your map as in the screen-captures below it is likely a Syndicate medallion.
Notice: If you get the variant of this challenge where you need to find a number of Syndicate Medallions without dying or being downed, you must be very careful - if you get killed your progress will be reset and you have to start all over again! Remember as Limbo you can always quickly roll into the Void plane and run away from enemies overwhelming you to avoid getting killed.