As the description says, you must complete 100 missions without any of your units dying or being downed.
This is cumulative, and tracks across all of your playthroughs,
although I'm not sure about the Jacked game mode as I have not played that yet (but I would assume it does...).
EDIT: The Jacked game mode does count. Thanks, The SCHWARTZ 00, for confirming.
Obviously, the easiest way is to play on Beginner. You will probably get this automatically if you're going for all other Achievements, but if you need help, I have listed things that I have found useful. Most tips you've heard for Insane, also apply here.
If you're playing on the easier difficulties, you can have your Supports focus on healing.
Your Scouts should go for frag grenades, stealth, and mobility.
Your Snipers should have abilities that maintain and increase their AP pool.
Your Heavies need strong overwatch, and high mobility.
Your Vanguards are best for their bayonet charge. It's high-damage, high-mobility, and a free action when upgraded.
On Control Side Missions, I normally put a Heavy at one supply point, and a Scout at the other. Their high mobilities can sometimes help you get to the supply point(s) on the first turn.
For Rescues, Scouts are best since they are excellent with grenades, and can disappear from sight.
Incursions and Sabotages are essentially the same. You have to eliminate all enemies, and you can take your time.
If you're not playing with Ironman mode enabled, you can reload checkpoint, restart mission, and even abort mission at any time if you feel like you need to redepoy with a different strategy.
Overall, this isn't difficult, it just takes a little time. I played the game on Experienced first, then Beginner with Ironman mode enabled, and then went back to doing Veteran missions on my experienced playthrough. After all that, I probably unlocked this at around 16 or 17 Veteran Missions completed. I hope that helps, and good luck.