Mega Man 10

As the achievement states, you must not use a single energy, weapon or mystery tank throughout the game. Although it can be difficult, there are some tips to help you breeze through this quicker.

1) Easy mode.

Don't be a hero, just whack it straight on to this mode.

2) Save states.

Really simple one. Just remember to save after every level you have completed without using any of the aforementioned tanks. It doesn't matter how many lives or continues you use as long as you don't use those tanks!

3) Use alternative weapons and items.

Remember that although you can't use the aforementioned tanks, you can use everything else! 1/2 damage tank is especially useful and remember the boss weaknesses.

Pump man = Thunder Wool (Secondary Strike)
Solar man = Water Shield
Chill man = Solar Blaze
Nitro man = Chill Spike
Commando man = Wheel Cutter
Blade man = Commando Bomb
Strike man = Triple Blade
Sheep man = Rebound Striker
Wily Boss 1 = Elec man - Wheel Cutter
Wood man - Triple Blade
Gemini man - Wheel Cutter
Ring man - Solar Blaze
Napalm man - Rebound Striker
Flame man - Water Shield
Slash man - Chill Spike (Secondary Strike)
Frost man - Commando Bomb (Secondary Strike)
Tornado man - Thunder Wool (secondary Strike)
Wily Boss 2 = Thunder Wool (Secondary Strike(Take out the claws with your Mega Buster first starting with the lower claw))
Wily Boss 3 = Rebound Striker
Wily Boss 4 = (part 1) Solar Blaze
(part 2) Water Shield
Wily Boss 5 = Chill Spike (Shoot the Wily without the red X on his head.)

After that lot, that's achievement unlocked!

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).