Update: Updates since the launch of the game have made it much easier to grind out coins in a reasonable amount of time without having to spend extra real money. Please see the comments for more detail. Thanks!
The two coin-related achievements are likely your last achievements in the game. When I finished three starring all levels of the first two episodes and grinding out bounces with Stella, I had exactly 2136 coins.
You earn coins in various ways:
1. Popping pigs - Popping pigs will randomly spawn a coin bubble. The bubble must be popped and the coin must be shot over (via sparkles) to your coin counter (so don't restart the level before that coin is counted).
2. Earning stars - There are certain milestones you can get by earning stars, including pictures and coin purses.
3. Defeating the Wall of Pig levels. There are 9 of these levels in the first two episodes, and defeating them will get you a chest full of coins.
Upon the game's release, the bulk of coins come from earning stars and defeating the wall of pigs levels. The coins you get randomly from popping pigs are infrequent, and you only get one at a time. When more episodes are released, you'll likely have an easier time earning coins in the new levels due to more coin purse milestones and wall of pigs levels.
However, right now, it is going to be a grind to get 5000 coins unless you buy them. Yes, purchased coins count as earned coins. You can buy a bulk pack of 2000 coins for US$19.99 and/or 900 coins for US$9.99.
Also, please note this game keeps track of any coins you previously spent, so don't worry about spending some to clear smoke or charge your hammer. You don't need 5000 at one time or anything. However, you might want to keep track of how many you spent in case you want to track your progress towards this achievement.
So anyways, the choice is yours: Grind them, buy them, wait for more episodes, or just walk away. Good luck!
