Ok, let me start by saying this is a pretty easy game, but getting all of the achievements can be somewhat time consuming. It all depends on how lucky you get. When you play the Classic style just use one controller and play as 4 human players. That way you can auction property for $10 instead of having to buy it full price. 

Playing as 4 humans also allows you to trade properties for whatever price you want. Also when you land on a property as a human player (no matter what player # you are) you still get the passport entry for that property. I will try to explain how to get each achievement the best I can below:

ACHIEVEMENT GUIDE

Everybody Starts Somewhere - 10 points

Buy your first property

Self-explanatory. Just buy the first property you land on.

Now You're On Your Way - 20 points

Own your first monopoly

Again, self-explanatory.

Climbing Your Way Up The Ladder - 30 points

Build your first set of houses. Classic mode only.

Same as 1 & 2. Just play as 4 human players and trade properties around to get monopolies.

The View From The Top - 50 points

Build your first set of hotels. Classic mode only.

Same as above.

High Roller - 10 points

Roll a double six

This will eventually just happen as you’re playing through.

Rolled To Jail - 10 points

Roll three doubles in a row and get sent to jail

Same as above.

Rolled To Freedom - 10 points

Rolled a double to get out of jail

Again, just play through. It will come.

Globe Trotter - 50 points

Land on every property on the World board

Easily done if you’re playing as 4 humans. Just buy every property and you got it.

Taking Sides - 50 points

Own every property, including any ports and utilities, down one whole side of the board

Easily done with 4 humans. Just trade properties around.

Transport King - 20 points

Own the monopoly on the transport properties

Same as above.

You've Got The Power - 20 points

Own the monopoly on the utilities

Same as above.

Deal Of The Century - 20 points

Form a monopoly as a result of trading

You guessed it. Just do this playing as 4 humans.

No Mercy - 20 points

Be responsible for the bankruptcy of another player

Just play as 4 humans, monopolize everything for player 1 with houses / hotels and wait until one of the other players lands on it.

Went For Broke - 10 points

Bankrupted yourself out of the game for the first time

This is stackable to No Mercy. If you are playing 4 humans just lose.

A Good Start - 10 points

Win your first mini-game in any mode of Richest

Easy and self-explanatory. Just follow the directions before the mini-game.

He Who Controls The Dice... - 50 points

Win every mini-game in a full game of Developer

Easy. Did this in one try.

Last But Not Least - 20 points

Win all the mini-games in a full game of Developer but don't finish first

Easy. Just win all the game and make yourself do something stupid to lose.

Taken A Chance - 10 points

Take your first property from another player using Chance in any mode of Richest

Just land on chance. This will happen as you play through.

Forcibly Formed - 20 points

Form a monopoly in any mode of Richest by taking one or more of the properties from another player.

This is easy too. Just wait until you can grab like 3 properties and there you go.

Dashed Hopes - 10 points

Break up another player's Monopoly

Same as above. When you can take someone's property just take one that’s part of a monopoly.

A Quick Victory - 10 points

Win a game of Developer mode Richest

Self-explanatory.

Faster Better - 20 points

Win a game of Industrialist mode Richest

Self-explanatory.

Becoming The Master - 40 points

Win a game of Tycoon mode Richest

Self-explanatory.

The Underdog - 50 points

Don't finish first in any mini-game but still win overall in any mode of Richest

This can be a little difficult. Just try to get second place in all the mini-games and you’ll still have an advantage.

From The Flames - 50 points

Come from last in the previous round to win overall in any mode of Richest

This is somewhat difficult. You just have to get lucky.

You Are The Richest - 100 points

Own every property on the board in any mode of Richest

This is somewhat difficult as well

Started Your Empire - 30 points

Build a set of houses in any mode of Richest

Once you have a monopoly just land on one of your properties next round. Pick a high die number to increase your odds.

Established Your Hold - 50 points

Build a set of hotels in any mode of Richest

Same as above.

Time To Collect - 10 points

Collect your first rent payment from any other player in any mode of Richest

Easy. Just wait for someone to land on your property.

Expensive To Stop Here - 10 points

Land on another player's set of hotels in any mode of Richest.

This just happens as you play through. Pick a high die number when someone has hotels.

Sight Seer - 20 points

Unlock a passport. Awarded to the passport holder

Once you fill up a passport by playing Classic mode with 4 humans you will unlock another one. Easy.

Jet Setter - 100 points

Fill all the passports. Awarded to the passport holder

This is the most time-consuming one. Just play as 4 humans and buy every property on every board. If it seems like you will never land on the last two (or whatever number) properties and keep skipping them just quit the game and reload. Your other passport entries will be saved so now you just have to land on the remaining properties. I always waited until about 4 or less properties then reloaded so the randomness would change. It took me about 1-2 hours per board to get all the properties playing as 4 humans.

Try Something New - 10 points

Unlock your first new board

Do this by filling passports. Easy.

The First MONOPOLY - 50 points

Get the same amount of money as the year MONOPOLY was released

Just do this while playing as 2-4 humans and trade a property for another property and add enough cash to the deal to make your total money $1,935. So say if you have $1500 just trade a property for someone else's property plus $435.