This is very easy, just time consuming.
All of these except the intel & headshots can be done on the second mission, 'Atlas'
KILLS
You will need to get 1600 kills, which can be easily obtained in the grenade range in 'Atlas'. Just keep retrying over and over again until you get it. Eventually you'll start getting excellent and perfect grades in it, this will also unlock the 'Grenadier' achievement if you do not have it yet.
HEADSHOTS
I believe you need to have 150 headshots, but I'm unsure. For this just play through the campaign and kill enemies with headshots and you should get by about the 3rd mission.
GRENADE KILLS
You will need to obtain 320 grenade kills, this can be earned the same way the kills can, if you get perfect over and over again in the grande range you should get about 25 more kills each time.
INTELS
Just look at a guide for the 'Ferrum Absconsum' achievement.
This can be done on any difficulty. If you make a new campaign, your stats will not reset, but if you reload checkpoint, your challenges will return to the previous number they were at that checkpoint. And just a little note for the grenade range, you can use Contact grenades for close up Smart grenade targets, and, if you act fast, you can destroy the first drone with a Contact grenade too.