I don't know why I'm so bad. I feel like when I start off attacking, MasterBot just puts up a wall and then builds his own attack overrunning me. But when I try to do that, he overruns me and I'm just nonstop building walls and can't afford any offense.
Example: http://play.prismata.net/?r=o8pnF-zZY6U
I start off aggressive and he just puts up a wall and ignores me, eventually overrunning me.
I'm no expert (you can find some on /r/prismata), but Tesla aggression looked like a reasonable counter to his heavy-economy opening. The execution looked non-committal, though: you kept droning, when you already have enough to churn out Teslas and Engineers forever; and then you built an Animus: you don't really have the economy to support all that tech. All this diversification takes off the pressure of your Tesla rush, giving your more-economic opponent plenty of time to outpace you.
Suggested changes: on your turn 3, you built BDD, leaving you with 13 gold for turn 4. That means you won't be able to afford Tesla+Conduit, which is what you really need to be able to Tesla forever. I'd recommend cutting a Drone, just building BD, so that you can Tesla+Drone on turn 4, and then follow up with more Tesla+Engineers. This is enough aggression that your opponent really can't make use of all the tech he's built: he has to defend himself. He can maybe get out two Tarsiers, but those are slow enough that you can just build a Wall once you've got enough Tesla pressure.
Some elaboration on this advice: somewhere in the tutorial or a new-player guide, it's recommended to, in most games, build like 10-15 Drones, and then
stop droning: building up an "economy" of attackers can be much more efficient than a real economy of Drones, in that it forces your opponent to spend money every turn to defend.
For example, in this game, your first Tesla Coil isn't very effective: it costs you an Engineer per turn, and your opponent an Engineer per turn because he can absorb the rest on his Wall. But every Tesla Coil after that is
very valuable: he has to build a Wall per turn to defend, while you just have to build an Engineer to keep it powered. So each Tesla Coil is, in a way, worth as much as three Drones and a Blastforge: it lets you spend 2 gold each turn in order to cost your opponent 5 and a blue, for a net gain of 3+B. Efficiency like this is how an aggressive strategy defeats heavy economy; trying to catch up on economy yourself is not nearly as effective, because you're not positioned to do so.
Once you get your third Tesla Coil up, your opponent probably has trouble even treading water, and then you can put off the fourth Tesla to diversify: build a Wall if he's gotten some attackers, or maybe drone up, or get that Animus you've been looking at, to add in Sentinels; or switch into Chieftains since you've already got the tech for it. The important thing is to do all this only
after you've put some real pressure on your opponent: one Tesla Coil is no pressure at all, but three is a lot.