Energy Tanks - Blue tanks with an E on them. When used from the item menu, your Energy is restored.
Weapon Tanks - Blue tanks with a W on them. When used from the item menu, your Weapon Energy of your currently equipped weapon is refilled.
Mystery Tanks - Blue tanks with an M on them. When used from the item menu, your Energy and all your Weapon Energy will be refilled. (Use it when you are full on these two things to turn enemies into useful stuff).
These can all be found throughout various stages. You can also buy them at the Shop.
Unfortunately, you can't use any of these for this achievement!
This becomes particularly easy when attempted on Easy mode, not only due to the sparse sprinkling of sluggish enemies, but also because there are occasional pickups that restore all your Energy and Weapon Energy (and you don't have to wait for the bars to go up either!). These are usually found where you most need them as well.
Personally, I found that the only time I really needed a weapon refill was towards the end of the second to last stage; the game provides one of the special pickups here (on Easy mode, of course).