General strategy

Character Selection
There are 9 Characters in trap gunner, although 2 are actually just clones of other characters but with a worse trap load out. Of the remaining 7 characters each has a unique gameplan and is a valid choice, although some have a harder time than others.

In high level play the capabilities of characters can be represented by how well they excel at denying large areas without actually being present (refereed to within the community as "Set-play" or "area denial"), how well they can control open areas and bridges (refereed to as "neutral"), and how strong they are at directly fighting an opponent (sometimes called "footsies" or "gunning")

Tico and REM/Van are both "jack of all trades" characters, able to play any style well but not excelling in any one area. Between them, Tico controls neutral better while REM/Van have higher damage

John Bishious and Dyn are particularly good at area denial due to their large amount of bomb traps. They also have an alright time in footsies since their guns have very high damage at close range.

Lou Richie and Abdoll have trap load outs that give them strong neutral control at the cost of weak set-play. Lou Richie's higher movement speed and large clip gives her better footsies than Abdoll, while Abdoll's knockdown shot and 2 gas traps give her more shenanigans.

Tenrou/Elg have a trap set that is rather weak in set-play and only okay in neutral, but their high movement speed, large melee range, and lots of ammo make them strong characters from a footsies standpoint. In other words they gun better than they trap.

Tier list
The generally agreed upon tier list looks something like this (Van raily and tenrou are omitted since they're weaker versions of Rem and Elg. While Bishous is generally considered better than Dyn they have different playstyles and thus are listed separately)

Top - John Bishious, Rem

High - Dyn, Lou Richie, Tico

Mid - Elg

Low - Abdoll

Tico is between high and mid, but she's closer to the bottom of high than she is the top of mid, all the characters are considered viable in a tournament setting except abdoll, although even she isn't totally hopeless.

The importance of switch traps and bombs
Switch traps and bombs are incredibly important, switch traps can be remotely detonated, which means just by having one placed you can prevent your opponent from ever setting foot into it's blast radius. If you put bombs around a switch you not only increase it's damage to potentially absurd levels but also increase it's range. Even without switch traps bombs make mines much more scary and can give you more control over the direction a body flies after activating the mine. Characters who don't start with a switch trap struggle with enforcing set-play and instead have to always be prepared to defend their traps from being defused. Characters who don't start with bombs struggle to deal enough damage to put fear in their opponents.

The potential damage of gas traps
Lou Richie and Abdoll trade switch traps for gas traps, which provide less utility than switch traps, but can allow for very high damage. Gas traps themselves do a decent amount, but their real power is their ability to limit movement. By slowing down a character you can force them into extremely bad situations where they're forced to take damage from shots or where they can't escape trap set-ups. Gas traps have high potential damage, but since they go off on a timer they're very easy to avoid. Gas traps can either be the worst trap or the primary source of a character's strength depending on how well the character (or player) can force an opponent into the gas.

Controlling bridges
Bridges and overhangs are the easiest way to defend against unit shots, so shutting them down can be very powerful. Bridges can often only be accessed by narrow corridors, meaning there are usually only 2 ways to get under a bridge. Movement traps, mines, and pitfalls are obviously good ways to cut off bridges. It's important to remember that the goal is to prevent an opponent from making it under a bridge, so putting a mine directly under a bridge wont actually solve that. If an opponent takes a mine before making it under the bridge they'll be knocked down and probably end up eating a unit shot as well as the mine damage. If they take the mine while under the bridge the unit shot will end up missing.