Medals, if needed, would be basically your avarage achievements. Rewarded from number of specific acts, for example saving lifes of allies, recovering artifacts or other valuable information, other acts of bravery... that's actually all that comes in mind right now. But yeah, medals equals achievements.
Ugh, please, no. Very much no. Please, don't ruin the whole medals thing equalling them to achievements.
1.Achievements are very mechanical. Do X N times, do Y in set conditions, etc. Medals are awarded. Sure, there are those things like '10 year service' medals and all, but overall they are not expected to be earned or acquired. One has to do something outstanding to get a medal, as their award is decided on case by case basis. You cannot just 'Okay, I'll need three more controlled overshoots with a field manipulator to earn the "Controlled Hazard" badge'. You do something, and then you may only hope that other people (mainly your direct superiors) decide that it has been a great doing (note the deliberate lack of 'enough'; once again, no set mechanism for acquiring these) and you've proven yourself worthy.
2.As such, medals have a very certain value to them, intrinsic to them by the very design - people do something worthy, and being awarded for that carries on some of that greatness to the award itself. Achievements, however, often have value by sheer virtue of being assigned value socially; if you feel them cool and interesting - sure, but if you don't, they don't have any value beside which you put into them. Think gold coins compared to modern day paper money. Sure, in all actuality, gold has as little immediate practical value as paper, but hey, at least it's shiny and considered valuable because other beautiful shiny things are made of it. (And that's not even taking rarity into consideration.)
3.And finally, I'm afraid that achievements have acquired a certain negative vibe to them, at least for some people; and for others, while cool, they might not be nearly as cool as medals and orders. Just one more reason to avoid connecting the two.
On the overall structure: I'd avoid having a rank of 'squad leader'. It's more of a position on a mission, and mixing up the two can result in confusion, so it's better to avoid it.
Also, I don't quite understand it. Specialist/Subcommander people - are we talking of Simus here (let's take her as a benchmark)? Or Adepts in Piecewise's structure? I'm confused again, I'm afraid.
One thing I would add though, would be the distinction between novices (mosty new recruits and lemmings) and privates/soldiers. Note that soldiers have no real authority over novices, but it could serve as a sort of 'rite of passage', indicating to the person being peomoted to soldier that (s)he is now recognized by his peers as a valuable and competent addition to the team.
Or if someone feels like becoming drillsargeant, that person could design vr courses and tests one must pass in order to achieve the next rank.
Note that this is purely optional, if people prefer everyone below squad leader to be in the same group, that's ok for me as well. Might foster team cohesion more, unsure.
Then it means that Piecewise's scheme was right, after all, with three lower non-commanding ranks. The first two exactly could be 'novice' and 'proven novice' as you want, and the third would be that 'more skilled, not commanding'.
Hmmm. Overall, somewhat amended Piecewise's systems seems the best answer to most of peoples wishes and needs. I'll try and post my take on the system later today.
I was mostly thinking of that scene in Aliens where a large part of the team is injured or unconscious and they are trying to decide if they should nuke the site from orbit.
Oh, that one is easy: one decides for all of them and shoots everyone who doesn't agree with him. And then gets promoted back on Sword. It's called willpower and determination, and is highly valued in leaders and officers.
(I have no idea how the issue was resolved in Aliens, having never seen the movie.)