There are only 2 points in the game where you can earn the achievements... the very start of the game and at the start of October 2001. These are the 2 times that you play the in-game soccer video game.

If you are trying to earn achievements at the start of the game, and need to start over, just quit to the main menu. Same with in October. The game only saves at the start of each of these segments, so returning to main menu and continuing will put you at the start of warmup or start of the match.

I would also highly recommend making a backup at the start of October. Just in case. You can find the save file in C:/Users/ YOURUSER /AppData/LocalLow/solimporta/despelote/NUMBERS/Despelote/despel.ote

Can be earned in either spot

• Gol - Score a goal - Self explanatory... score a goal in either warmup or during the game. Any goal.
  
• Golazo - Score from outside the box - There are 2 "rectangles" on the playing field; you need to score from outside of the further one, not the closer one! This did award oddly for me, as I kicked from outside the further box, then kicked it again just outside of the goal... and it awarded. So hopefully this also awards a little easy for you, too!
  
• Auto Gol - Score an own goal - Kick the ball into your own net
  
• Gol De Arquero - Score with the goalkeeper - Get the ball and head towards your own goal. Kick the ball gently to your goalie and let them take the ball. As the goalie, RUN towards the opposite goal... you will throw it forward, but be fast enough to catch back up without switching focus to another player. Re-grab the ball, continue running, and score that goal! If you walk with the ball out of the box as the goalie, you will not be able to get the ball back; you must run. Thanks to @Teresolis for the push towards figuring this out.

Can only be earned at the start of the game

• Listo - Score 3 goalds during warmup in 30 seconds - There is no warmup period in October, so this has to be done at the start of the game. It only worked for me when playing on keyboard; on controller, it kept exiting the warmup before I had a chance to score 3 goals. The goalie in warmups is much harder to score on than the goalies during the matches!

Can only be earned in October

• Si Se Puede - Win the match - Score more goals than the other country after the full 90 seconds
  
• Invicto - Don't let the other team score - Exactly what it says... finish with the other country having 0 goals. This should not be hard, as the AI is quite bad.
  
• El Gol Del Tin - Score in the last 5 minutes - You have to score a goal on the other country between 85:00 and 90:00. Just try and time it right. Might take a few tries.
  
• Goleada - Win by 5 goals - This is kinda tricky, since controlling the player and the ball is imprecise. Aim to have 2, if not 3, goals by the end of the first half. The first half is harder, because your mom blocks the game screen for 10+ seconds. When I got it, I scored 2 in the first half, 4 in the second. My advice is to take the ball away from the defender, move slightly left or right of center, and then head straight towards the opposing goal. Run right into the goal with the ball or kick it from very close to the goal. The goalie should only block you if you are running straight at him or shoot the ball straight at him.
  
• Jugamos Como - Lose the match by 15 goals - You have to score 8 own goals in the match, as an own goal counts for 2 in this game. Again, the first half is harder. I found this easier than Goleada... I managed 4 own goals in the first half, and then 6 in the second. For a score of 0-20. Similar to scoring on the opponent, do the same thing but score on your own goalie. This should be even easier... just don't run straight into your goalie and you should score the own goal.
  
• Despelotini - Kick a ball outside of the stadium - After the match ends, you'll exit the stadium but still be in top-down third-person view. As you enter the town, go up. You should hear the sound of a soccer ball being kicked back and forth. Find the 2 people kicking the ball, take it from them, and kick it. Thanks to @GiacomoP for this one.