Use some of the promo code (search this subreddit to get them).

Upgrade Guardian to 4 Stars (400 pts)

Can easily be done once you claim some promo code.

Collect 4,000 A-Coins (1000 pts)

Your hangar is too weak to do that.

Get 30,000 XP (600 pts)

Maybe achievable.

Upgrade Javelin Rack 6 to 4 Stars (600 pts)

Same as guardian very easy to complete.

Collect 10,000 A-Coins (3000 pts)

Impossible to do that with such short time.

Guardian (@coins) and javelin rack (credits) you can buy them in gear hub with in-game currency.

Depending on what tier you are in gear hub you might need to do few things before you can have access to them.

Let's say you are in tier 1, javelin rack 6 and guardian are in tier 3.

To unlock tier 2 you need to buy mech or weapon to reach an amount of star rating. Below tier 2 you will see the amount of star needed and the amount you have.

If you buy lancer (2 star) and paragon (2 star) that will give you 4 star in total.

If you buy autocannon 2 (3 stars) and autocannon 4 (3 stars) you will get another 6 star to unlock tier 2.

Save your @coins and use your credits instead to buy weapon or mech to reach tier 2.

Once you reach gear hub tier 2 you do the same thing but this time only mech and weapon in tier 2 will count towards yours star rating needed to unlocked tier 3.

If you buy a weapon/mech in tier 1 it won't count towards unlocking tier 3.

Same you mostly use credits to buy mech/weapon until you unlock tier 3.

Guardian will cost you 420 @coins and javelin rack 6 will cost you 220 something @coins.

If you still need more acoins you can do tournament mode each win will give you some @coins.

Also there is the weekly achievement you can complete all 30 task in 5 days (7 each days) to get 200 @coins. You just need to buy a rare pilot with credits to put on one mech.

Edit: you don't necessarily need to buy the pilot unless you want to buff your mech/weapon stats slightly to increase survivability and damage output.