Unlocking this achievement is fairly simple, but there is A LOT of confusion regarding what counts and what doesn't. There is also a Heroic Deed that ties into this achievement, and you need to complete the Heroic Deed to unlock a different achievement. There are three types of events you can complete:
1). You can rescue groups of Imperial Guard soldiers at various points during the campaign (there are currently 5 of these in the campaign), and you can also find them randomly on certain types of open world missions, namely Purge, Hunt, and Bunker Buster.
2). You will occasionally find blue teleport beacons that will transport you to unmapped secret areas of the map. These are usually small one or two room areas that contain an Elite enemy and a loot chest or reliquary.
rarely you will come across an allied psyker and a group of Imperial Guardsmen. You will get an objective to "protect the psyker until the warp gate closes" along with a timer bar. You can simply destroy the warp gate and go on about your business. No need to hang around for the timer bar to run out.
Now, for Stalwart Servant achievement
, all three of these types of events will count, as the description of the achievement is "complete 25 events". However, apparently only #1 and #3 are considered a "side mission". The Heroic Deed of the same name (Stalwart Servant), requires you to "complete 25 side missions", and ONLY the first and third types will count toward it.
The reason this is important to note is that completing the Heroic Deed unlocks a skill tree, and therefor ties into the following achievement, as well:
So to give you an example, I unlocked the Stalwart Servant achievement when I was only showing 11 of 25 in the Stalwart Servant Heroic Deed. And just for reference, I had the best luck finding side mission on the Bunker Buster open world missions, and on Tarot Purge missions.