For completing the "Beaver Team" achievement on your own, while building a skillset you need to focus on sprinting speed (because you only have 5 seconds to take down 5 trees), shaped charges and saw efficiency.

You need to be at least lvl 55 for the skills and you don't need an infamy level.
NOTE: you need to own the Yakuza character Pack for the perk deck.

There is no need for skills in the Mastermind tree as it has nothing to do with either speed, charges or saws.

For the Enforcer tree i chose the following skills:

In the Shotgunner tree we focus on the skill "Close By". This allows us to hipfire while sprinting. I will explain the usefulness of this skill later on.
Besides "Close By" we focus on the saw efficiency in the Ammo specialist tree.

For the Technician tree there's only one skill you need: Lock N' Load

Just work your way up to "Lock N' Load" in the Opressor tree, because this one lets you saw while sprinting. (thanks Lee Sun Jin for suggesting this skill!)

For the Ghost tree there are 3 skills you need, see below:

The ones in the Artful dodger tree are for instant speed bonusses.
The one in silent killer is a different story. This one will give you a speed bonus when you lose your armor.
To get this achievement you need to destroy your own armor efficently. Here the skill "Close by" comes in handy. Because you can hipfire while sprinting with that skill you can destroy your own armor while sprinting to a next tree. This combined with a shotgun with explosive bullets is a must-have.

For the Fugitive tree i chose the following skills:

The skills in the revenant tree are for bonusses when revived. You could just focus on the skill running from death, but "Feign Death" makes trying to ghet the achievement a bit less time consuming.

In the Brawler tree you focus on the "Frenzy" skill, the other skills are fillers (filled it up for the players without infamy level). This lets your health drop to 30%. Which is necessary for your perk deck.

I chose the "Yakuza" perk deck (Yakuza character pack). Because this one gives me more movement speed while my health is under 50% (because of frenzy it is).

Primary:

Saw
• Durable blades

Secondary:

The judge shotgun
• HE rounds

I used an armor with an armor rating as little as possible.
Two-pieced Suit (Two shots with the judgeon the ground and its perfectly gone. NOTE with the frenzy skill aced, i did not check it without it being aced)

Throwable: Grenade
Deployable: Trip mines
Melee weapon: any

The first thing you do is walk to the first tree.
Then down yourself, you will get up either by the "Feign Death" skill or by your crew mate.
When you are revived instantly place the shaped charge, because you only have a speed boost for 10 secs with the skill "Running from Death".
Then run to the far right tree (seen from starting point) and while you run, shoot twice at he ground with your judge.
When your armor is gone, swap to the saw and saw the far right tree.
Then run to the other side of the road and saws that tree.
Turn left, saw that tree an finally run straight to the last tree and saw that one.

It will take a few tries but it is possible ;)

P. S. English is not my first language, so sorry for grammar or spelling mistakes i may have made :)

Good Luck!