The first two paths are really easy. A Pokémon around Lv 60-70 can easily grab both of the candies. The real challenges are path 3 and 4.
However, type advantage can be used to against the towers: for line 1, Rock-type Pokémon resist all the attacks. For line 2, Ground-type Pokémon resist all Electric moves and Rock- or Steel-types resist the Hyper Beam attack from Jolteon. For line 3, Ghost-type Pokémon are immune to all Fighting-type attacks, and Psychic-type Pokémon may do well too. For line 4, Magneton, Victini, Hypno or other Psychic-resisting types will do.
A extremely good method to beat it and get the achievement, all while using 3 Pokémon, is to use a Golem, a Ghost-type Pokémon, and a Psychic-type-resisting Pokémon. First off, no level 70 Pokémon can be used, and you have to beat the fourth path first; you won't get the achievement if you don't meet those requirements. Second, make sure your Pokémon all know Double Team and Substitute. Third, use Golem on the first two paths, the Ghost-type on the third path, and the "anti-Psychic" on the fourth path. The benefits are as follows: Golem can resist Normal- and Fire-type attacks very well, Ghost-types take no damage from Fighting-type attacks, Double Team increases evasion, and Substitute means less damage taken by the Pokémon that used it.
Using Wide Guard and Tailwind for all the columns can work very effectively; it requires 2 Pokémon, but any level can do it. Doing it this way I have completed it with a Mr. Mime Lv. 1 and a Butterfree Lv. 30: send in Butterfree first, then Mr. Mime with a small time gap. This wastes the attack on the Butterfree allowing Mr. Mime to set up his guard.
Another good way is using 2 Vaporeon with Aqua Ring, an Electrode with Protect (Because it is the fastest Pokémon), an Onix with Rock Polish (it makes Onix faster), a Blastoise with Iron Defense, and a Golem with Defense Curl. Remember, these Pokémon NEED TO BE LEVEL 70 OR LOWER to get the achievement.