Best way to do a lot of these, especially healing ones etc would be to have 2 people, one hunter and one monster but this guide is for solo only.
THIS WILL ONLY HAVE CHARACTERS THAT GET YOU THE ACHIEVEMENT.
If the mastery DOES NOT say MONSTER then you can damage anything, DEFEND is the best for this with the minions.
RESTART, if the MONSTER is about to die then RESTART, saves a good few minutes and all you stats count as they happen.
If you have the RELOAD perks then you should be using that.
Revives can be done on RESCUE though remember if you need them with DAISY, don't have LAZ and visa versa, ALTHOUGH you can hotswap if somebody gets too close and wait till DAISY gets there and hot swap back. If it says 2 revives in one match then as soon as you get the allotted number restart.
As mentioned by others, the KRAKEN is best for headshots, specially on DEFEND.
If its just hit then use the BEHEMOTH (use the the red skin if you have it, it makes it easier to spot).
Again as others have said make sure you use custom match and unless stated put low creatures and whatever map perk suits you. Also favor HUNTERS.
If the MASTERY isn't based on feats in 1 match try and focus on 1 thing, it makes the MONSTER last longer which over time equates to a whole less loading.
If you swap characters you do not seem to get stats for mastery on both, only the character you chose.
Best way to level up MARKOV is solely in defend. This should not be too hard.
Best way again is DEFEND. Residual burn will take a bit of time but in DEFEND you get 2 minions every couple of minutes to burn up.
DEFEND, no surprise.
RESCUE for anything DAISY related. Tier 3 restart after you get 2 revives.
HARPOON & MACHINE PISTOL - DEFEND.
GRIFFIN (In Process)
SOUND SPIKES/GAUSS - DEFEND - With the sound spikes I focused only on sound spikes, hotswap and take down the SHIELD if the monster is highly damaged. GAUSS self explanatory.
With LEVEL 1 MONSTERS some people say to use maps with FORCE FIELD but I chose BEHEMOTH and CLEAR SKIES. But also spend alot of time on one map and you will learn the layout. If you try and get 2 spots before you trap the monster you can possibly get 5 before you have to restart.
DEFEND, you can achieve all of ABES easily in DEFEND.
HANK (in process)
DEFEND or MAPS with TOXIC CLOUDS for shielding damage. TIER 3 SHIELD has to be cumulative, but if the players becomes incapped it restarts. This will be easier online IMO.
LASER CUTTER/ORBITAL - DEFEND
HUNT - UAV just focus on this. TIER 3 you can hopefully TRAP the MONSTER after the second UAV and then get 3 whilst it is trapped, then you can average 5 a restart. Follow the MONSTER so you are kinda close but not close enough to trap, also as soon as you have UAV fly it straight out and be ready to tag the MONSTER as soon as its untagged. Everything else can be done in hunt, specially TIER 3 as when it levels up you can focus on the damage side, but if your struggling with SENTRY/MISSILE the use DEFEND.
DAMAGE AMPLIFIER/RAIL CANNON - Easiest in DEFEND.
DUST TAGGING - TIER 1 change custom settings to have high wildlife. TIER 2 easiest in DEFEND. TIER 3 I used CLEAR SKIES and BEHEMOTH, the BEHEMOTH can get from one side to another quickly so use other MONSTERS if you prefer, BEHEMOTH is just easier to spot.
DEFEND or maps with TOXIC CLOUDS. TIER 3 HEAL is cumulative, but if target dies then its resets.
Everything else can be done in DEFEND.
LAZARUS DEVICE - RESCUE - use hotswap to stop teammates rescuing people. TIER 3 RESTART after 3 saves,
PERSONAL CLOAK - RESCUE - again hotswap to get better stats, TIER 3 - restart after 3 saves.
CAIRA (in progress) Most likely best online.
HEALING GRENADE LAUNCHER -RESCUE /maps with TOXIC CLOUDS. (Hotswap to get better stats)
ACC FIELD - HUNT.
NAPALM - DEFEND or whilst doing ACC FIELD in HUNT.