I currently have a level 2 melee druid I would like to multi class with a monk. The objective would be to increase the damage of my natural attacks when in wild shape form to become a massive mauler. Which monk archetype and specifically which feats could I get to increase the damage of my unarmed strikes.
This doesn’t work
Monk’s bonuses to your unarmed strikes don’t apply in any way to your natural attacks.
The best way for a druid to get more damage with his natural attacks is to take more druid levels—your wild shape will get better, you will get better spells to buff with, and so on. Monk has almost-nothing to offer here. Wisdom-to-AC while wild shaped is kinda decent, but you can always get barding for your combat forms. Even the single level of monk you would need to get the AC bonus costs too much to be worth it—AC is the weakest defense in the game, and spells are the best defense (and offense, and utility, and everything else) in the game. Slowing down your spells for a level to get some AC is not a good choice.
Now, monk also does have a number of bonus feats, which is nice, ish. From your other questions, they’re feats you want to take. But you can just take them as a druid, even if it will be slower. And because spellcasting and wild shape are so good, and so important to what you want to do, delaying those feats a little is definitely the right play for improving your “mauler” abilities.
There are probably a few corner-cases where, say, you knew you weren’t going to get another level of druid spells, you might want to take a level of monk for them. Depends on the precise level, like if you were taking your 14th level and knew you weren’t going to make it to 15th, a level of monk might be more valuable than a couple spells per day and another wild shape per day, since you already have a good number of both at that point. But prior to 14th, I would probably prefer more or better daily wild shaping over the monk benefits, and definitely for 20th, at-will wild shaping is way better than anything you’ll get from a single level of monk. And any odd level other than 19th is definitely out—access to spells one level higher will always be better than what monk has to offer.
A multiclass to monk could help you increase wild shape damage AFTER you have wild shape, but you have to take feral combat training to get the full benefit of flurry of blows. By default, monks must be unarmed or use monk weapons to use flurry of blows. Natural attacks are not unarmed.
Feral combat training has a prerequisite of weapon focus and improved unarmed strike, which is problematic. Because you will get improved unarmed strike for free when you take the monk level, you need to wait until you take the monk level to take feral combat training. You could take weapon focus claws at third level, if your GM allows you to ignore the fact that you don't have any claws until fourth level.
All of this discussion about qualifying for flurry of blows becomes irrelevant if you take the monk archetype maneuver master. Because you are multiclassing and would have a relatively low monk level, your bonus maneuver would not be very strong.
KRyan makes some decent points. You are delaying your progression of wild shape in order to take these monk levels. Wildshape for animal forms maxes out at druid level 8. Until at least then, you will lag behind a full druid in wildshaping ability. You have to weigh the benefits of monk levels against having a bigger wild form, and better spells. If you spend your entire time in wildshape, and do not take natural spell, you have already effectively given up your spells.
If you are still focusing on grappling, as you were with earlier questions, a single monk level will jump you to the top of the grappling feat tree. The second monk level would give you fewer returns for your investment.