Avery Carrington's missions become available after the mission, "Riot". He has three missions in total, all available from the construction site in southwest Vice Point. The final mission is not available until you gain proper access to the Vice City Mainland/West Island.
Four Iron
Tommy climbs into Avery's limo. After some Texan sayings and an offer of whiskey, Avery gets down to business. He talks about "claiming dirt", or competing for land, and he has learnt that one of his rivals that owns a substantial amount of land is playing a few rounds of golf at the local course. The Clubhouse has security, meaning that he and his bodyguards won't be fighting back with weapons. He wants Tommy to suit up, go into Leaf Links and take the baron down.
Head to Jocksports nearby to obtain the Golf Club Outfit. You will have to park up to get more information for this mission. You are told to go through the security gates and beat down on him, but if you head over to the west side of the road leading up to the Clubhouse, you should see a ramp. Park a car next to it, jump on the car and then onto the ramp. You can use your weapons to take him down, making this mission very easy.
It is then up to you to head to the driving range and take down the land baron. After killing him, you'll have to get away from his bodyguards and out of the course the same way you came.
Mission Passed: $500
Demolition Man
Avery talks to Tommy about an office block, which is "in the way" of Avery's plans for the land it is being built on. He think that the job will suit Tommy's skills in demolition, and Tommy sets about it straight away.
Head to the Top Fun Van down the street from the construction site. You are using an RC helicopter to carry bombs to four soft spots inside the construction site. There are three levels and the ground floor, which have one target each. Once you pick up one of the bombs by closely hovering over it, you have seven minutes to plant them all.
In your way, they are construction workers armed with hammers, and security guards armed with Pistols. They will need to be dealt with as you head through the site. To kill them, direct the rotors of the RC helicopter towards them, and that will take them out. To make the mission easier, plant the first bomb at the top, and make your way down to the bottom. The staircase is easily found, entered to the south side of the central block of the site.
By working your way down, you should take down mostly all of your enemies, making it easier rather than facing them off at each level of the site. You will have to hover directly over the barrels in the center of the targets to correctly plant the bombs. Otherwise, you will have an easy time once you've got over the controls of the chopper.
When you have planted all four bombs, you see it go up in a massive explosion. The mission will be successful.
Mission Passed: $1,000
Two Bit Hit
Tommy jumps back into Avery's limo, and is introduced to Avery's protege, Donald Love, from "Grand Theft Auto: III" fame. He tells Tommy that there's nothing like gang warfare to drag down and cheapen land, and he has spotted that the Cuban and Haitian gangs are not too friendly with each other. A Haitian gang-lord was murdered, and his funeral is today. He wants Tommy to masquerade as a Cuban thug, and take out a key Haitian gang member at the funeral in order to cause an inevitable war.
Head to the Little Havana Streetwear store in the Cuban neighborhood to pick up the Cuban outfit. You need to head to the funeral parlor next to the Pizza Parlor in Little Haiti, where the hearse and the Haitians are located. If you have a sniper rifle, you can head into the alleys nearby to take out the target, making sure you are spotted beforehand, and not have to take substantial damage. When the target is dead, get out of Little Haiti.
Mission Passed: $2,500
