Respect is a statistic that represents how your fellow gang members look at you in the game. As you gain more Respect, you will be able to recruit more gang members to join you while doing a mission or something else. The majority of the missions in the game will reward you with some Respect, but it isn’t enough to actually max out the bar and get the maximum Respect for this trophy/achievement. Upon completing the mission Doberman, you will unlock turf wars, which allows you to take over rival gang territories. These will be represented as colored sections on the map, with purple being Ballas and yellow being Vagos.
Taking over these enemy territories provides the biggest boost to your Respect, since you get the bonus for the actual territory, but also from killing the gang members, too. It is best to do these alone and not recruit fellow gang members, since them dying has a negative impact on gaining Respect. You also gain some for killing law enforcement, so going on a rampage against the police can also be helpful, especially when you gain access to something like a Rhino or Hunter later on in the game. Buying expensive clothes can also help, so a place like Didier Sachs is ideal for this.