Using Cheese & Garlic Mints can give Leon a very powerful initiation tool: not only will your enemies be pulled towards your team, but they will also be unable to use any escaping/defensive abilities they might have.
If you don't have Basic AI Chip, leaving a clone inside a hide area will grant vision to you and your teamates.
Leon may forgo health upgrades. With the ability to cloak and get into or out of practically any situation, he can get in, deal massive amounts of damage, and leave without a trace.
One of the first abilities you will want to upgrade if you want to maximize your DPS against droids and 'nauts is your Backstab Blade. It will help you tremendously, since you will almost always get a backstab or two on your first strike, and you will get a lot more if they start to run away. However, if your goal is to have high overall damage and be effective against turrets, Chainsaw Addon is a better option.
If you're actively in an engagement and have Surprise Party Mask upgraded, quickly cloak and uncloak for a higher damage slash.
Always make sure to go around crossfire while cloaked, you might be invisible but enemy projectiles and area of effect damage are still issues. It is very easy to be nailed by a lone dynamite and immediately killed.
When you're stalking an enemy, if you see him start to attack a turret, sneak up from behind him, stand still, and wail on him. This will keep him trapped between you and the turret for a short period of time, maybe until he dies, if he doesn't realize that you are standing in the way quickly enough.
Jumping around an enemy will let you avoid a lot of unneeded damage. If you have the Backstab Blade equpped, jump behind them repeatedly to boost your damage output tremendously.
With either Aggressive AI Chip or Blow Up Doll, Leon is able to push two lanes at once. Simply leave a clone in one lane close to enemy droids and push the other lane yourself. Using Basic AI Chip makes this tactic more efficient.
Even when Leon's invisible it's still possible to hear his footsteps. Some players turn off the game music and increase sound effects volume for this sole purpose.
Jumping erratically around Leon may be useful when trying to evade Tongue Snatch.
The cooldown on Leon's Cloaking Skin doesn't start until invisibility is broken. If you see him uncloaking, keep in mind that you have a few seconds to attack or even kill him before he can cloak again.
Don't let the minimap fool you! Leon's clones appear as a 'naut there.
If Leon is using a clonespam loadout (which involves sending clones to attack your turrets over and over), keep in mind that his cloak will most likely be unavaliable when you find him. It could be a good idea to either kill him or force him away.