This guide is roughly follow the same structure as anon's Fidel Dungeon Rescue Achievement Guide:
https://steamproxy.net/sharedfiles/filedetails/?id=1584753672
I felt theirs was the easiest to understand.

Bark. Required for a few achievements. Use to make enemies face you so bite them from behind. Also used to extinguish candles.

Proceeds to the next level when standing on the exit stairs. Swaps the entrance and exit when standing on the entrance stairs. The latter is useful when needing to optimise.

Undo step. Of course you can just step back on your leash, but this is useful for undoing a bunch of steps.

Opens the menu.


Most achievements are awarded immediately when the condition is met. There's no need to have a valid path to the level exit. This means you can unlock the achievement, then undo and create a new path to the exit.

Level ? of 15 are the first set of levels you must complete. I recommend completing this set first to open the rest of the game, then come back for the achievements.

Eat 4 Plants
Levels 1 to 3 are usually the levels where plants appear. Keep restarting these floors until you get the floor you need. Plants refer to the big flowers, and not the ones in the achievement icon. Example:


Party is Over
Level 4 is an alien rave party. Kill all the small aliens.


Overweight Rescue
Keep restarting the plant levels until you get one with the red square and star tile. Bomb the square, extinguish the candle underneath and jump in the portal that appears on the star tile. Example:

In the new room, eat every hot dog and then finish the rest of Level ? of 15.

Chew a Mimic
Barking next to a chest to reveal its contents and then attack it from above if it's a mimic. Rewards 5XP.

Nobody dare touch my grandma
Level 5 (usually) has the Robot Dog kidnap grandma. Bomb the button instead of stepping on it and finish the level for the achievement.

Secret Level
Level 10 as five candles. Bark at them to extinguish the candles, then jump into the portal.

Checkmate
Access the Secret Level above, then defeat the king which involves attacking all the other pieces without taking damage.

Good Dog!
Clear Level ? of 15 with the regular dog.

After beating Level ? of 15, enter the red portal to access Underworld ? of 10.

No Zapping
Finish the boss level (Nightmare) without using any diamonds. They can still be collected, but make sure none are used against the boss.

Fidel
Clear Underworld ? of 10 with the regular dog.


Dead dog CAN bark
On the screen after beating Nightmare, bark crossing into the afterlife.

These can be done any time after beating Level ? of 15.

Flashback
On the hub screen, bark at the tennis ball so it falls into the pit, then begin Level ? of 15.

BAD DOG!!!
Push the tennis ball down the stairs in the Flashback level above. Then continue collecting the tennis ball on every level and complete Level ? of 15.

Gift from Beyond
On the hub screen, bark at the tennis ball so it falls into the pit, then begin Underworld ? of 10. Collect the tennis ball on every level and complete Level ? of 15. On the final screen, push the ball into grandma's hands.

These can be done any time after beating Level ? of 15. The bonus games are across the bridge on the left side of the screen. From the bottom they are Cemetery, Puzzle, Centipede, and Bones.

Dying a lot is fine
Start the Cemetery game and die several times to the ghost.


Who you gonna call?
Beat the Cemetery game and on the last screen walk over the trap in the middle and next to the button. Press Ctrl+Shift+F3 to spawn the ghost and press the button when the ghost is over the trap to to capture it.
Much thanks to geryllaz for sharing the method to do this on the current patch.

King of Puzzle
Beat the Puzzle game mode. 6 screens in 6 minutes. Optimising is the focus here, as often the best solution is required to open the exit. If you are having trouble, screenshot the puzzle, pause the game and solve it elsewhere first.

King of Centipede
Beat the Centipede game mode. 5 screens in 4 minutes. Best way to beat this mode is to figure out which sections need to be bitten (as to not leave leftover sections) and work from there. The bomb may help, but isn't required to beat any level.

Daily Challenge XP Overdrive
Bones are daily puzzles. One puzzle a day equals one bone a day. Overdrive is awarded for solving any daily puzzle with more than the required XP. Significantly easier on the current patch as Zombie Dog has 4 hearts. There's also lots of examples in the discussion forums.

319 Bones
This achievement requires 319 bones, so that's completing 319 daily puzzles. Unlike other puzzles, daily puzzles are fixed. Because of this, some puzzles are unsolvable after the latest update.
365 Bones - Fidel Dungeon Rescue Daily Solutions[fidel-dailies.web.app] has solutions to all of them. I assume it's created by the creator of this guide:
https://steamproxy.net/sharedfiles/filedetails/?id=2210997965

Unlocks after clearing the Puzzle game mode once. He can be selected by eating the hot dogs on the hub screen.
Robot Dog doesn't gain XP, instead he needs to use his 9-coin ability to purchase additional hearts. His 3-coin ability destroys all enemies in the current row and column.

Robot Rescue
Clear Level ? of 15 with Robot Dog.


Not A Real Stair
Clear Level ? of 15 with Robot Dog. On the screen after pushing Grandma onto the elevator, use the lightning attack to attack the Underworld boss and try to go up the stairs.


Robot Ending
Clear Underworld with Robot Dog.



Unlocks after clearing the Centipede game mode once. He can be selected by eating the hot dogs on the hub screen.
Zombie Dog doesn't use first aid kits and heals by performing triple combos or killing larger enemies. His 3-coin ability scatters worms in adjacent cells and 9-coin ability scatters them all over the screen. Worms are used to help string together combos.

Zombie Rescue
Clear Level ? of 15 with Zombie Dog.


Zombie Ending
Clear Underworld with Zombie Dog.