If you save these for after you complete all of Solo mode, you'll have a good understanding of the handful of level maps and the way the game likes to variate them. There's only a few maps, and during missions you play different portions of those maps, sometimes in reverse.
Usually for the High Value Target missions, you play the entire map, usually with big chunks of it being empty to simply pass through. For the most part, the maps are played in reverse, with you spawning in usually a place where you previously would end the map, and work your way backwards towards the HVT.
If you're not worried about score, you can skip a lot of enemies and save a lot of time if you know the maps. The guide arrow will help you for the most part, until you're in the section the HVT is actually in (then it fades away).
HVTs have about double health of normal enemies, so try to snipe them or focus on headshots if you can, and try not to get close. Enemies in this game have infinite ammo and what seems like no need to ever reload. If they spot you, they'll continuously shoot in your direction, not really allowing you a moment to counterattack. Some levels have the HVT tucked in a corner, so I made sure to equip all of my characters with Team Frag grenades, in case I ever had the opportunity to just blow up the room they were sitting in.
The levels have no checkpoints, so if you die, you start from the beginning. Because of this, try to be careful and take your time, and don't take too many risks. Animal's grenade launcher (unlocked when he hits level 9) is a really useful weapon, especially if you are good with sniping with the pistol (thank goodness for auto aim).
Usually if you aim the crosshair at an enemy's head, when you hit the L button to ready your weapon, the game will usually lock onto the enemy's head. Eventually you should get used to this, and be able to rapid fire headshot many enemies, understanding this.
You need 5 stars in every solo mission (ranked) to unlock all the HVTs (final HVT unlocks at 180 stars), or you could contact someone who has them all and ask them to "share" the HVT unlock with you via the "NEAR" feature of the playstation Vita. 5 stars isn't necessary on all missions for any trophies, so if you can find someone (don't ask me, I'm selling it since I just completed it) who's got them, it'd make your life easier. Personally, going for 5 stars each mission helped me gain the skill I needed to defeat the HVTs.
Thanks to deimosplaysgames on YouTube for the video walkthrough of this mission.