In order to reach the point where you can work towards this achievement, you will have become quite proficient in Breach Mode. There are many different viable approaches. I've included a video walkthrough that features a severely handicapped avatar in a hostile environment where enemy levels are maxed out in all three categories. This is so it will be relevant to a wide variety of play styles.
To reach Tier 4, you must complete 18% of Tier 3 and have cleared a path to the exit node. Note that you can have completed the Data Master Achievement before reaching the 18%. Conversely, you can reach the 18% before clearing a path to the exit node to Tier 4.
Once in Tier 4 any server on the map counts towards this achievement. This includes regular server map servers, Santeau servers, Data Transport servers, etc. Unlike the Data Disciple, Expert, & Master achievements where you have to clear all server map servers in a Tier, for this achievement, you only have to clear five servers of any type. In other words, the achievement unlocks once you complete any five of the following Tier 4A servers--note that DF4_BYLINE is a Darknet file server and will only be available if the associated Darknet case has been unlocked.
S01_STOCKADE, S02_STOCKADE, S03_STOCKADE, S04_TALONPIKE, S05_LAVAWALL, S06_CORTEX, S07_CLAYMORE, S08_CAISSON, S09_GARRISON, S011_EMBARGO, DF4_BYLINE
Note: It helps to work on or complete the below achievement before the Tier 4 servers. The expansion items you get by doing so level your avatar up by an order of magnitude.
WhiterValkyrie has a good guide that helped me:
Edited to add (29 Jan 2018) - Video Walkthrough: I didn't provide a video walkthrough when I first posted the guide because different players have their own preferred play styles. By the time they reach Tier 4, there is considerable variation in their approaches. To address this issue, I'm adding a walkthrough where the avatar is minimally configured and enemy levels are maxed out. The avatar is set at minimum health & energy. It is equipped with basic weapons and carries no curatives, modifiers, or expansion kits.
The intent is to clear five servers set to the highest hostility with a weak avatar. Players, at their discretion, can choose to play against lower level AI hostility, increase health and/or energy, and/or make use of better weapons, curatives, modifiers, and/or expansion kits. With much less of a handicap, they should be able to use the routes depicted in the videos to clear the servers relatively painlessly.