Having had both metatarsal stress fractures and Achilles trouble I can tell you that soft shoes aren't the answer.
Regarding the metatarsals you just want a shoe that is flexible without forcing you up on your toes. An inflexible shoe that doesn't want to bend with you is an obvious problem. Softness in shoes here can be a sneaky problem. If the forefoot is too soft the balls of your feet (under all toes) will sink into the cushioning. When the balls of your feet sink in like that it exacerbates the bending at the joints on either side of the balls of your feet. This can put more stress on your metatarsals.
With your Achilles you need to come to terms with whether or not your legs can handle minimalist running or not. This is based on how you were raised and your current physiology. If you can't run minimally without calf stress and Achilles trouble, then you need to simply get shoes with reasonable offsets like 10-12mm. Higher offsets lessen the elasticity required from your Achilles. I'm serious that you need to do some self-evaluation on this front and be honest with yourself instead of trying to meet any modern trends that have nothing to do with your individual physiology. On the softness front here you need to know that soft shoes can be a problem for the Achilles. This is for two similar reasons. At impact you sink into the soft cushioning some. This is a problem for two reasons. One, your heel stack height and offset become lower than advertised once you sink. So you'll go flatter than the advertised ratio if the heel is soft, which may demand elasticity from your Achilles you don't have. The second problem is that at impact (especially if you are a heel striker at all) there are major mechanical things happening in your heel to absorb impact and transfer it into forward motion. Your Achilles pulls in one direction while reacting with a force in the other direction. Ideally you want this snap to be quick and efficient. Very soft heel cushioning can extend the duration of the impact and draw out the time where the Achilles is stretching in one direction while preparing to go in the other direction. This makes the vulnerable mechanical moment of change take on more risk in the transition.
I'm not recommending you change to rock hard shoes, but shoes people describe as "responsive" might help you. These are typically shoes with a little bit of a firmer cushion that offer you a tiny amount of give at impact without actually feeling like a pillow or soaking up your impact. You may need to grow a little accustomed to it, but if you give it a chance you'll give your body an opportunity to run lighter and more efficiently by spending less time on the ground during impact periods.