Important to note, taking a look at the guide you quoted, as LYR is "Independent", you can undermine by killing target ships of powers that are aligned with one of the superpowers. However, if you want to undermine another independent power, then undermining is done by pirating the respective transports - very tedious compared to just killing.
By killing, flights of one or two targets you may be able to kill before the FSD cooled down (depending on the ship you bring and your skill, of course), and you get 30 merits per kill. Pirating for the cargo, you must not kill the targets, but hatch-break them and scoop up the (illegal) cargo (10 merits per container), which makes you a target for other pirates (actually not sure about that one) and the normal system police force (about that one I am sure). While as long as you keep killing just the enemy power ships, your standing with local system police and factions does not change.
Also important to note, despite what the game tells you, you can not just kill the transports, but also the power-specific militia. Like I am currently undermining Edmund Mahon for the Smurf princess, so the game tells me to kill Alliance Bureaucrats in EM control systems, but killing Alliance Enforcers equally counts toward the undermining score.
Some general undermining tipps,
- generally about your scanner, to find ships in supercruise, going faster gives you a bigger range on the scanner (game logic ; same seems to apply to the speed of the enemy ships)
- usually I can find one batch of enforcers and/or bureaucrats dropping to the Nav Beacon, very helpful in biiiig systems
- if you intercept a flight of 2 or three targets, always interdict one of the escorts, and always first kill the escorts, as once the transport dies, the escorts jump away
A kind of subjective suggestion, if you are just in for the merits, I'd suggest to attack control systems of Edmund Mahon, as with 137 control systems he is by far the fattest pig and absolutely deserves a thorough spanking.