All of those achievements are obtained by progressing in the campaign, and are unmissable.

Finish the 1st level.

Finish the 4th level.

Finish the 1st world.

Finish the 2nd world. (both will be triggered at the same time)

Finish the 3rd world.

Finish the 4th world. (both will be triggered at the same time)

This section is about achievements that you gain naturally by upgrading your aircraft.

Upgrade any aircraft completely.

Buy a new aircraft.

Buy the last aircraft in the game, unlocked in the 4th era.

This section is for the achievements you get through destroying an certain number of enemies of each type. Like the previous category, you will obtain them naturally through the game.

Destroy your first building.

Destroy 200 aircraft.

Destroy 200 buildings.

Destroy 200 turrets.

Destroy 500 tanks. No, this is not a typo, for some reason you need to destroy more tanks than anything else in the game.

This section contains the achievements that does not fit in any other category, and are the most likely to not be done if you rush through the game, though they still are easy.

Restart the same stage 5 times in a row. Note that this can use menu restarts, not just gameover restarts.

Launch your first superheavy bomb. Bombs are consumables that drops extra powerful bombs onto the enemy, and this is the most powerful version of them.

Own 5000 credits at once. You need at least this much to buy the last aircraft in the game.