These are all the challenges you unlock as you rank up:

Season 4 Officer Challenges
C4: Get 5 Kills with C4 (1,500 XP)
Sniper Kills: Get 300 Marksman or Sniper Rifle Kills (15,000 XP)
Merciless Killer I: Get 10 kills without dying 3 times (6,000 XP)
Precision Airstrike: Call in the Precision Airstrike killstreak 5 times (1,500 XP)
Triple Killer I: Get 25 Triple Kills (3 rapid kills) (15,000 XP)
SMG Kills: Get 100 Kills using SMGs (3,000 XP)
Pistol Kills Headshots: Get 5 Headshot kills using Pistols (1,500 XP)
Head Swivel: Get 2 Headshots within 60 seconds of each other 25 times (15,000 XP)
Bounty Hunter: In Warzone, complete 50 Contracts (9,000 XP)
Claymore: Get 5 Kills with Claymores (1,500 XP)
SMG Headshots: Get 50 Headshot kills using SMGs (15,000 XP)
Proximity Mine: Get 15 Kills with Proxy Mines (6,000 XP)
Backup Plan: Get 30 Kills using your Secondary Weapon (1,500 XP)
Battle Hardened: Get 300 Kills while using the Battle Hardened Perk (15,000 XP)
Scrapper: Get 30 Kills with weapons from other players (3,000 XP)
High Five: Get 50 Kills with weapons with 5 attachments (1,500 XP)
Fury Killer: Get 7 Fury Kills (4 rapid kills) (15,000 XP)
Semtex: Get 15 Kills using Semtex (9,000 XP)
Spotter: Equip the Spotter Perk and Destroy a total of 7 Enemy Killstreaks, Equipment and Vehicles (1,500 XP)
Downtown: In Warzone, start Contracts in the Downtown area 30 times (12,000 XP)
Two To Tango: Get 125 Kills using a weapon with 2 attachments (6,000 XP)
Assault Rifle Kills: Get 50 Kills using Assault Rifles (1,500 XP)
Armor Shopper: In Warzone, Purchase the Armor Plate Box from the Kiosk 25 times (15,000 XP)
Snack Attack: Kill 2 or more enemies with a single piece of lethal equipment 3 times (3,000 XP)
Shotgun Headshots: Get 7 Headshot Kills using Shotguns (1,500 XP)
One Trick Pony: Get 250 Kills using a weapon with 1 attachment (12,000 XP)
Smoke Grenade: Kill 30 Enemies while near smoke (9,000 XP)
Cluster Strike: Call in the Cluster Strike killstreak 5 times (1,500 XP)
Streaker: Kill 30 enemies using Killstreaks (12,000 XP)
Cold-Blooded: Get 100 Kills while equipped with the Cold-Blooded Perk (6,000 XP)
ADS: Get 15 Kills while Aiming Down Sights (1,500 XP)
Gas Mask: In Warzone, survive in the gas for 25 seconds (12,000 XP)
Shrapnel: Get 7 Lethal Equipment Kills while using the Shrapnel perk (3,000 XP)
Gulag Controller: In Warzone, start Contracts in the Gulag area 3 times (1,500 XP)
Long Shot: Get 40 Long Shot Kills (12,000 XP)
Heads Up: Get 25 Headshot kills while using your Secondary Weapon (9,000 XP)
Pillager: In Warzone, Collect your loadout 3 times (1,500 XP)
LMG Kills: Get 275 Kills while using LMGs (12,000 XP)
Killstreaker: Call in 5 Killstreaks in a match 5 times (6,000 XP)
Champion: In Warzone, Finish in the top 30% 2 times (1,500 XP)
Crusher: Run over 30 Enemies with Vehicles (9,000 XP)
Warhead: Get 50 Kills using Rocket Launchers (6,000 XP)
Slider: Get 5 Kills while sliding (1,500 XP)
Helpful Hand: In Warzone, Revive a teammate 15 times from using the Kiosk (9,000 XP)
Quickscoper: Get 25 Quickscope kills (3,000 XP)
Assister: Get 20 Assists (1,500 XP)
Revenant: Get 20 Kills while injured (9,000 XP)
Dead Aim: Get 15 Headshot kills that are Longshot (6,000 XP)
Double Killer I: Get 3 Double Kills(2 rapid kills) (1,500 XP)
One Shot: Get 50 One-Shot kills (9,000 XP)
Support Box: Use the Stopping Power Field Upgrade 15 times (3,000 XP)
Weapon Collector: In Warzone, Pick up 10 weapons (1,500 XP)
Molotov Cocktail: Get 20 Molotov Kills (9,000 XP)
Dead Silence: Activate the Dead Silence Field Upgrade 20 times (6,000 XP)
Prison Fighter: In Warzone, win your Gulag match 2 times (1,500 XP)
Ammo Provider: In Warzone, Purchase a Munitions Box from the Kiosk 10 times (9,000 XP)
LMG Headshots: Get 20 Headshot kills using LMGs (3,000 XP)
Vehicle Driver: In Warzone, drive vehicles for 5 minutes (1,500 XP)
Ammo Drop: Use the Munitions Box Field Upgrade 40 times (9,000 XP)
Four Piece Dinner I: Get 3 Quad Feeds(4 uniterrupted kills in the kill feed) (6,000 XP)
Assault Rifle Headshots: Get 5 Headshot kills with Assault Rifles (1,500 XP)
Four Leaf Clover: Get 200 Kills using a weapon with 4 attachments (9,000 XP)
Trophy System: Deploy the Trophy System Field Upgrade 20 times (6,000 XP)
Launcher Kills: Get 3 Multi Kills using Rocket Launchers (1,500 XP)
Hardliner: Get 3 Kills without dying 20 times (6,000 XP)
Thermite: Get 7 Kills using Thermite (3,000 XP)
Deployable Cover: Use the Deployable Cover Field Upgrade 5 times (1,500 XP)
Three Cheers: Get 150 Kills using a weapon with 3 attachments (6,000 XP)
Stun Grenade: Stun 7 Enemies using the Concussion Grenade (3,000 XP)
Tune Up: Deploy your Field Upgrade 15 times (1,500 XP)
UAV: Call in the UAV Killstreak 30 times (9,000 XP)
Launcher Destroys: Destroy 15 Vehicles (3,000 XP)
Protector: In Warzone, Use 25 Armor Plates (1,500 XP)
Bloodthirsty Killer I: Get 5 Kills without dying 10 times (9,000 XP)
Hunter: Get 20 kills while crouching (3,000 XP)
Finisher: Execute 2 Finishing moves (1,500 XP)
Inbound: Call in 50 Killstreaks (9,000 XP)
Shotgun Kills: Get 150 Kills using Shotguns (6,000 XP)
Artillery: In Warzone, Purchase 3 Killstreaks (1,500 XP)
Throwing Knife: Get 15 Kills using the Throwing Knife (6,000 XP)
Distance Marksman: Get 2 Longshot kills within 60 seconds of each other 5 times (3,000 XP)
Zero Tolerance: Get 25 Kills while using a weapon with 0 attachments (1,500 XP)
All Clear: Destroy 30 pieces of enemy equipment (9,000 XP)
Ghost: Get 75 Kills while equipped with the Ghost perk (3,000 XP)
Close and Personal: Get 5 Melee Kills (1,500 XP)
Pistol Kills: Get 75 Kills using a Pistol (6,000 XP)
Headhunter: Get 20 Headshot kills (3,000 XP)
High Alert: Get 25 Kills while using High Alert (1,500 XP)
Frag: Get 15 Kills using the Frag Grenade (9,000 XP)
Hipster: Get 30 Hipfire Kills (6,000 XP)
Well Equipped: Get 7 Kills using Lethal Equipment (1,500 XP)
Flash Grenade: Blind 20 Enemies using a Flash Grenade (9,000 XP)
Killer: Kill 75 Enemies (3,000 XP)
Recon Drone: Mark 10 Enemies using the Recon Drone Field Upgrade (1,500 XP)
Stim: Recover 1500 Health by using the Stim Tactical (9,000 XP)
Sniper Headshots: Get 30 Headshots using Sniper or Marksman Rifles (6,000 XP)
Munitions: Get 5 Hipfire kills with your Secondary (1,500 XP)
Point Blank: Get 20 Point Blank Kills (6,000 XP)
Survivor: In Warzone, survive without being downed for 20 minutes (3,000 XP)
Sprayer: Get 2 Hipfire Kills within 60 seconds of each other 5 times (1,500 XP)