How to make a 40* eudemon?

Step 1 : Pick a starter

First of all, you need a good starter. Hatch about 40 eggs and pick one with decent sub-attributes, since sub-attributes are fairly hard to build, but they are very, very important for questing.

(e.g. if i'm building a Venus Sage, i will look for a Venus with either high HP GR or MDef GR)

Step 2 : Start composing

Now you have your Major, start main composing at Aderes till your eudemon asks 2.8* minors. Don't touch ini and sub attributes just yet. If you hatch any high ini/sub attr. euds, put them on your warehouse for later (name them 'sub' or 'ini' according to there stats).

Note: Whether you use clovers here is up to you. Know that, when you use clovers, star requirement for minors will increase faster (higher requirement at lower star), but your eudemon will get more star marks every compose and its main attributes will be better.
So, if you are building a eudemon for stats (e.g. a lanir for questing), use clovers, if you are building a eudemon for stars (e.g. scrunch/sizzle as guardian), don't use clovers, as you will have to spend more to get it 70*.

Step 3: Ini-Main-Sub-Composing

Now your eudemon asks 2.8*, it's time to start doing ini and sub composing. If you followed Step 2, you will have some good ini/sub attributes eudemons on your warehouse now.
You can always check the stats of your eudemon at the eudemon appraiser, next to the evolution oven at the market, or, if you're lv120+, simply by clicking the magnifying glass on the top right of the detail window of your eudemon.
Once you composed all the ini/subs from your warehouse, start main composing again. If you hatch new good ini/subs, you can compose them immediatly. Keep doing this until your eudemon asks 4.8* minor requirement.

Step 4: 34* is near

After you completed Step 3, your eudemon will be close to 30*. Keep up main composing with 4.8*s as long as you get around 10 starmarks per main compose. You will notice at a certain point that that #starmarks/compose will drop to 3-5 starmarks.
Once your eudemon reaches 30*, start using Super Reborn Cr ystals (SRCs) too.

Note: There's a common misbelief that eudemons with alot of rebirths are less valuable than a eudemons with little rebirths. This is false. Maxing out rebirths takes very, very long (since you can use only 4 SRCs every week = 80 rebirths every week). The sooner you start, using SRCs the better

Keep this up until your eudemon reaches 34*.

Step 5: Orb/Agate

Now your eudemon is 6* away from 40*, it's time orb compose and agate compose. You will need 10 Universal O's (total of 280 eps in the mall). You can access the orb/agate compose window by clicking the eudemon altar button, just above your BP.

Do 5 orb composes and 5 agate composes. It goes like this for both:

1st: 80 pts
2nd: 70 pts
3rd: 60 pts
4th: 50 pts
5th: 40 pts
total: 300 pts

1 pt = 1 starmark.

Step 6: Have fun with your 40*!