These achievements require that you complete all three goals in every level of the game, including all the secret and hidden levels. Each level has three goals to complete, which are objectives that you must satisfy. Goals can only be viewed from the pause menu (tap the button in the top right corner of screen while in a level) or in the level completion screen. Example goals are completing a level within a certain time limit, without using power-ups, by only entering holes a given amount of times, without getting spotted, or causing cats to smack into walls. The good thing about goals is that you can complete each one on a separate playthrough of the level (i.e. they do not all need to be done simultaneously). Most of the goals are easy, but a few here and there can be frustrating and will give you trouble. For levels that have safe holes, use them to your advantage. They basically act as checkpoints. For example, if you are working towards the goal of not being spotted and you enter a save hole, exit the hole and get spotted and die, you will respawn back at your save point and can continue working towards not getting spotted. Some levels have two parts (they seem like they should be two levels) and when you enter the second part of the level you will also get a checkpoint.
There is no complete guide for the game out there as most guides just show you how to complete the level, which is always simpler and easier than doing so while completing any of goals. Below I have compiled a listing of helpful images, strategies, and videos that you might find useful as you progress through the game.
There are XX regular levels, 7 secret levels, and 5 hidden levels, for a total of XX levels. Boss levels do not have goals so dont worry about them (though they each have their own achievement). See "Easy Way Out" and "Explorer Mouse" for the locations of the hidden and secret levels as they contribute to these achievements as well. From the level-selection screen, you can tell which levels you have already completed all three goals on as the dot for those levels will have a blue and white badge on it. Earning all three goals on all the levels will unlock these three achievements.
All of the Secret and Hidden Levels (pictures)
Complete World 1 Strategies (Images/Text)
All World 1 Video:
Complete World 2 Strategies (Images/Text)
All World 2 Video: