Getting to level 40 is a grind that takes many hours no matter how you do it. The only ways to level up are to complete an operation and to collect the 80 pieces of intel, which you'll be collecting as you play. Each intel gives you 200XP and is located right near the resupply box in the middle of every phase you do (there will always be 1 for 1 phase 2 for 2 and 3 for 3). Simply press back when you find the supply box to determine the intel location, though do note that if you only need photos or audio logs that you must wait for the intel to be a photo or an audio log
Once you've picked up the 80th piece of intel, you can officially then only get XP from completing the entire operation. If you all die during a phase even if you've completed 1 or 2 phases within the operation, you will still get 0 XP. Killing enemies in the underground and the "increased kill XP" stat on gear also don't count toward your rank either
(NOTE: If only 1 player is remaining, run away and let everybody else quit the game and restart. When they sign in from the main menu it will put them directly back into the operation at the start of that particular phase and you'll just need to run back to where you were. This works if for any reason your game happens to glitch or your team dies)
Each level from 1-39 you will receive a sealed cache when you level up. When you go from rank 39 to 40, you get the B.L.I.N.D. gear set and the ability to purchase 229 weapons and 268 gear from the UG vendor, though no sealed cache
The most XP you can possibly earn for an operation is 9,500XP for a 3 phase heroic with 5 directives on, though beware this is essentially unheard of to even the most elite players and something you will almost surely not be doing to level up
The fastest way to level up I've found is to do Hard operations with 3 phases and 5 directives, which will net you 6,000 XP per run and take about a half hour each. To do this, the leader must be at least lvl 35 and all other players can be whatever level (either matchmake or go to LFG as a low UG level). Additionally, ALWAYS skip any scene that tells you to 'investigate' or 'locate' anything until you've actually arrived at the objective and the timer disappears as this will speed your very repetitious runs up dramatically (NOTE: The XP rate is the same for 2 phases as it is for 3, so at lvl 30 you'll officially hit the per phase XP cap. The only benefit of the extra phase is spending ever so slightly less time in loading screens between operations)
In case you haven't leveled far yet, keep in mind that for a hard 2 phase with 3 directives will net you 2,880XP, 3,400XP for 4, and 4,000XP for all 5. This figure will simply have 2,000XP added to it for if you play a 3 phase
To get directives it's best to let someone else be the leader and spend their intel while you accumulate your own. Each phase will give you 1 directive intel when you kill the boss, so remember that when you're running 5 directives that the leader is still losing 2-3 directives each run instead of gaining them depending on if you're doing 2 or 3 phases. Also, each day you can complete 1 hard operation for 10 phoenix credits and 1 directive intel as well as a challenge operation for 20 phoenix credits and 3 directive intel (they stack if you do it on challenging for 4 intel and 30 phoenix credits)
NOTE: XP required to level up has changed following a patch to the game. Thus, it will take less XP to level up and you'll be able to get this achievement several hours faster now
Best of luck to all grinding this achievement. Hope this guide helps speed things up for you and let me know if there's anything else I can add!