Paw Paw Paw only saves the items you have upon level completion or death, but not when you quit a level to map or the title screen.

Knowing this fact, we can easy exploit this and get the following achievements without spending to much money (food). It just takes a little bit of time.

Kaboom
Throw 100 bombs

Beast Master
Ride 100 mounts

1) Enter the Forest Outpost level (or any that sells the item) and use all of the none bombs, or mount eggs you are carrying.

2) Now use the shops to buy as many bombs and eggs as you can carry. Then leave Forest Outpost.

3) Enter Bounty Hunter's Camp (again, any level will work) and use all of the items. Press Esc and exit to map.

4) Keep on repeating step 3 until you unlock the achievements

Note, this can also be done for Gulp Gulp Gulp (use 100 potions), but you should naturally get that through out the course of playing the game.

If you have the means to do so, you could also record a macro to repeat this action so you don't have to do it manually ;)