Here is a fantastic guide on how to quickly complete all missions available in Just Cause 2 by Americanchoirboy.

He also explains various strats, tweaks and tips on how to get around Panau as fast as possible, as well as some game settings on how to properly optimize JC2 for speedrunning. He is also working on optimizing the routing without the use of the black market, removing the need to spam with the rocket launcher.

There are over 50 videos in this guide, so if you wanna head over to his youtube channel and avoid loading them all in here, I highly encourage it: https://www.youtube.com/channel/UCK5g2FFKcigVVx7keZScz2Q

His videos are extremely helpful for anyone wanting to get into speed running Just Cause 2, especially for an All Missions speed run:

Super Sling Tutorial

A Second Amendment

Above The Law

Airport Troubles

An Officer and A Hitman

Black Gold

Boys With Toys

Breaking And Entering

Bridging New Contracts

Can I Get A Witness

Casino Bust

Chemical Compound

Clear Skies

Death From Above

Driving Miss Stacey

Free Trade

Fry Me To The Moon

Head Of State

Helicopter Hangaround

Hell On Wheels

Holy Smoke!

I Want To Break Free

Jumping Parole

Keeping The Flow

Mercenaries Must Die

Mountain Rescue

Nothing To Declare

Oil For Blood

One Deadly Sin

Paparazzi Pursuit

Paradise Valley

Pilgrimage

Pirate Broadcast

Political Debate

Power Surge

Pulling A Jeremy

Rico's Day In Court

River Runs Red

Rocket Science

Save The Forest

Siphoning Gas

Smugglers Do Run

Stop The Press

Stranded

Taking Candy From A Millionare

Taking Out The Dishes

Taming The Beast

Three Kings

The Broader Scope

The Mile High Club

The Red One Or The Blue One

The Setup

The White Tiger

Ups And Downs

Welcome to Panau