I have played a ton of games over the years and in 99% of them there is some kind of a quest system. I've been thinking for a while what could be done here, this game is really wierd to work around for quests and I guess this is why I couldn't find a straight forward topic on it. But now I think I have found a solution to this and I am excited to share it!

I. The quest system
The base idea is to battle a certain type of ship. The very first quest that every player must complete in order to unlock the others is to battle 10 LF. The battle itself is going to be happening on a special place in the universe that is called The Nebula. The Nebula has no coordinates and it is always located on 20 000 distance from any colony/moon. Flight time is always 100%. The only way to get to The Nebula is to start a qeust and you can only fight the quest fleet that you are going for. Quests can be started from any colony/moon. Normal lanx rules apply for those missions.

Once a quest is completed a new one is unlocked. Each quest requires to kill a certain ammount of ships of the corresponding kind. Here is an example of what the count looks like in my head:
10 units
25 units
50 units
75 units
100 units
etc.
Those numbers apply and are available for all battle ships (there will be no quests for killing cargoes, probes, sats or recyclers). The progression will look the same except for the RIPs, where the quest will start with 1/2/5/7/10/15/20/25/50 and continuing with the above sequence afterwards.

II. Quest page
A new quest page needs to be added. In that quest page ofc will be some text, mainly focused towards new players to explain them the basics of battles, how to find the battle simulator and how to use it. Also there MUST be an example of what to send for the very first time! There is also the need of 2 drop down menues - one to select the type of ship you want to go on a quest for and one for the difficulty count. The numbers here must be going downwards, but the default option should be the last defeated fleet.

III. Rewards
Now there are 2 types of rewards I have in mind - one that is tear based, but minor and you get it every time and one major reward for first time completeing a quest.

The first time completing quest reward is simple - you get the DF of the DEFEATED fleet only spawned at your quest launched coordinates and you can collect it from there. Note that any lost ships from your side are note included.

The tear rewards I kinda based on the current expedition rewards, and the formula should be
TEAR REWARD = TEAR LEVEL * 125.000 Metal, 62.500 Crystal and 41.666 Deuterium

Tears:
T1 - 0 to 5.000.000 damage dealth
T2 - 5.000.000 to 15.000.000
T3 - 15.000.000 to 25.000.000
T4 - 25.000.000 to 50.000.000
T5 - 50.000.000 to 100.000.000
T6 - 100.000.000 to 250.000.000
etc...

IV. Additional info
- Launching a fleet towards The Nebula consumes 0 deuterium, no matter the size
- The quest fleet in The Nebula has the attackers WASP technology
- A quest mission consumes expedition slot. Active quests missions cannot exceed available expedition slots.
- A maximum of 5 quests can be done per day. Quest count resets at 00:00 server time
- DEBATABLE! There is 1% chance to obtain 1% of the ammount of defeated ships
- A variety of fleet count for the quest fleet could be added. I was thinking for +-10%, but the initial fleet is always 100% count untill defeated.
- Player's destoyed ships in quest battles are not recoverable and no DF will be spawned for them.

I think I covered everything that was in my head. I was also thinking of adding personal titles into this, like for example after completing 5 different quests for destroying 100 units a player can get "Avanturist" tile, or after defeating 5k or 10k destroyer ships to get a "Destroyer" title. Getting the titles was what was going into my head when I named it achievement-ish system, but I don't want to overthink it right now. I would like to see some feedback before going for that.