You've played this game quite a bit, and want to get the 4,000k in 13 days medal, which is the hardest medal in the game by far.
Below I'm going to give a description of what items are the best for what aspects of your rocket, when they're needed, and how to upgrade them.
(Note: When I say "10" that means lvl 10. When I say "+10", that means max level plus 10)

I'm going to assume you have El Fuego, Steamshot, and Pingu Ballon.
I'm also going to assume you've got A LOT of the bonus shop items unlocked. This achievement requires some grinding, so you should have all of them to level 3 at least. I also had premium spring, turbo compressor, improved fuel, and traffic control all the way to "MAXED". You also need the upgrade bonus items to MAXED in order to boost everything to +30.

It's actually very simple. You need gross amounts of money, and the omega items.
Get the omega spring, omega rockets, omega boosters, and el fuego. Boost everything to max +30. Waste many minutes of your life watching a penguin soar.

Glider is the first one you get. Then you get El Fuego, and you camp on that the rest of the game. El Fuego is incredibly over powered in this game. Honestly, when fully upgraded, it's better than a fully upgraded omega shuttle, even when considering the lack of a stage slot. Weird I know.

Start with the slingshot, then the tilt cannon, then the steamshot.
Steamshot is better than nuclear reactor, orbital cannon, and big bertha. It's better to start with, and after upgrading. You CAN win with steam, in fact I don't know if I could have won without it. (The Steam at max+30 is the same as Omega max+10, but the steam is about $500k cheaper! Which means you pretty much need steam.)
While the steam launcher takes a bit of skill, it's forgiving. You don't have to get perfect to get a really good launch.

You start with a lvl 2 balloon, then the rocket, then you use sonic burst.
Sonic burst is amazing. Once you can afford it, it's worth it, and you can use it up until 4 million and win. Just keep upgrading it, and it maintains it's worth consistently.

This is the hardest one, because they usually feel kind of useless, but can affect things quite a bit.
This might seem weird, but pingu balloons and repellers are the best boosters.
To start out, use all your money BEFORE boosters. Then with what's left, get pingu balloons (to the best efficiency).
At day 11 or so, you should start inventing in repellers, because the junk in the air starts ruining your runs (I had TWO bad runs in the first time I won, so it's not "that" big of a problem).

It seems like you should try to keep all your items roughly the same worth (hold control and hover over the item to see how much it sells for). For example, when having all items worth about 30k each, you get 1,410k, but if you cut funding in half on the sonic bursts, and spend that money on the body, or the launcher, your rates go down about 100k or so. Or, if you cut funding on the launcher and body and give it to the sonic bursts, your rates go down about 100k or more. Seems like keeping the amounts roughly even works the best, maybe spending a bit more on the launcher.

I did a whole bunch of tests (which I won't bore you with all the details), and here's some things I found.
The omega parts are completely useless for everything, except going extreme distances. You'll only ever use these for getting to distances like 10,000k. For everything else, you should use El Fuego, Steamshot, Sonic Bursts, Repellers, and Pingu Balloons.
The money turbine is basically useless. The extra money you get is not as much as the extra money you'd get for more distance, if you spent the cash on better gear rather than the money turbine.
The fuel canister is also useless. It's heavy, so the weight actually counteracts the benefit from the fuel.
Fins are great IF you're not using the sonic burst. If you're using the sonic burst, wings are kind of useless.
Basically all the boosters are pretty useless. You might get a few more km out of them, but I'd say repellers and pingu balloons (to offset the weight of the repellers) is always your best bet.
Here are the only reasons you should use anything other than the sonic burst.
1. You're too poor.
2. You're going for extreme distances (like 10,000k)
Sonic bursts earn you WAY more money (considering how long rockets take to actually do there thing, you could do multiple runs, at lower distances, to get way more money at a faster rate).
Also, the 4k in 13 days is absolutely possible with only sonic bursts.

Here's a screenshot of the set up I used on the 13th day, where I got to 4,000k, without ever spending any sardines, or using any consummable items. Also, I didn't even fire my third Sonic Burst. So yeah, not only is it possible, but it's easily possible.