The first loot chest is in the small group of buildings southwest of the Arena, behind the "We Got This!" billboard. Approaching the Seraph Vendor, there is a tall ladder on the right that ascends to a platform with the chest on it.
The second loot chest is outside of the map exit to The Beatdown, behind the Torgue Bike billboard above the Catch-A-Ride station. The ladder is behind the hanging banners, and leads up to a series of girders that provide access to the chest.