So on advice from a friend AceMcCloud
to get this achievement, you have to play Arena first, something specific like Big Team Battle or Slayer (Team Arena and Elimination do not work) though and check your Game Stats before and after a win in Arena, you need to see your "Matchmaking Victories" increase, I think the safest way to check is using the Xbox App on a smartphone, go to your achievements, Halo 5: Guardians, and you'll see it on the stats above achievements.
Once your "Matchmaking Victories" in the Xbox App on smartphone increase after a BTB or Slayer, switch to Warzone Firefight and after each map the victories should continue to increase, and if you get Raid on Apex 7, Escape from A.R.C. or March on Stormbreak then they will count towards Warlord.
Some other advice AceMcCloud
gave me to avoid freezing, after every game, let the ending animation finish, don't press anything until the scoreboard comes up, so don't skip if it shows an award animation. Once the scoreboard comes up, quickly press Y to bring up your REQs, then press B to exit out and B again to get back to the matchmaking screen. If you want to put on a Boost, quickly press A and select it, now don't press anything else until the next match loads up and you can control your Spartan. If you're desperate to open REQ packs you earn, do it on the computer at the Halowaypoint website instead. Doing this I seemed to avoid it freezing when previously it was freeze after every game when I was opening a REQ pack or just pressing B to exit the scoreboard and go back to the matchmaking screen.
I did also have the achievement tracker on, and found it would update once the scoreboard came up.
Games (All done within 6 hour window before this post)
Raid on Apex 7 - Win - Didn't count (as with the previous 4 or 5 Firefight games I had done, although they did count for Cry Havoc and Not Your First Rodeo and progress towards Tour of Duty, but they only require you complete them, not win them.)
Matchmaking Victories didn't increase, as had been the case for previous 4 or 5 Firefight games, and indeed also Team Arena and Elimination games.
Then played a BIG TEAM 1 FLAG CTF as advised
Matchmaking Victories increased, and switched back to Warzone.
Escape from A.R.C - Win - Counted
Raid on Apex 7 - Win - Counted
When the map FINALLY
March on Stormbreak - Win - Counted
Once it was working, I didn't want to stop... so I stayed up all night to get it. Achievement unlocked!
Halo 5: Guardians Service Record
Arena, 35 Games, 21 Wins
Warzone, 22 Games, 21 Wins
(All Warzone Firefight, not played regular Warzone at all).
Halo 5: Guardians Xbox Live Stats
Matchmaking Victories, 18 (Only!)