First of all, if you're supporting swarm, don't enchant individual creatures, support them with totems, Etherian Life Tree, Acid Ball, Rust, Marked for Death, and/or Call of the Wild. Second, you have to be careful how much you invest in a single threat, particularly when you don't have other threats available to back it up.
To my mind, the Beastmaster is all about efficiently building just enough economy that he can continually apply more and more pressure over time. Quick Summoning, Ring of Beasts, Enchanters Ring, Battle Forge, and Lair are the main reasons this works. The Lair in particular lends itself to aggressive placement, and, thus, to aggressive plays. It's tougher than other spawnpoints, and lets you start applying pressure very quickly.
Here are some Beastmaster openings you can try:
Battle Forge Rush:
Turn 1 (19): Sprint to NC (Near Center) -> Battle Forge (11)
Turn 2 (20): Deploy Ring of Beasts -> FD (Face Down) Brace Yourself -> Steelclaw Grizzly (1)
Turn 3 (10): Deploy Enchanter's Ring -> Advance to FC (Far Center) -> Thunderift Falcon Pet -> FD Bear Strength (1)
This allows you to launch a fast attack with a pair of durable threats (the Steelclaw Grizzly and your mage), but with some small creature support. You have a bit of economy from Battle Forge, but it's certainly still possible to stall out a bit against mana denial.
Bear Spam:
Turn 1 (19): Mana Flower -> Mana Flower (9)
Turn 2 (20): Ring of Beasts -> Steelclaw Grizzly (2)
Turn 3 (13): Enchanter's Ring -> FD Brace Yourself (10)
Turn 4 (21): Steelclaw Grizzly -> FD Bear Strength (4)
If you play a bear every other turn or so, you can launch a pretty strong attack, although it will be slower than a Battle Forge Rush. This opening will have to be adjusted more than the previous one if your opponent is aggressive, but you have plenty of mana to work with.
Falcon Swarm
Turn 1 (19): Sprint to NC -> Lair in FC (4)
Turn 2 (13) [2]: Deploy Thunderift Falcon Pet -> Advance -> Thunderift Falcon (1)
This opening sets you up for the fastest attack, and has enough economy to keep you going to some extent from the Lair, although you have to be really careful of zone attacks and Chain Lightning. One thing to keep in mind is that you can opt to use Timber Wolves or Emerald Tegu as the basis for a Lair play instead of relying on Thunderift Falcons. They won't be able to apply pressure as quickly, but they are far less vulnerable to swarm counters.
Meditation Amulet Lair
Turn 1 (19): Advance one zone -> Lair in NC -> Meditation Amulet (0)
Turn 2 (9) [2]: Deploy Emerald Tegu -> FD Brace Yourself -> Meditate (3)
Turn 3 (12) [2]: Deploy Dire Wolf -> Meditate -> Leather Gloves (3)
Here you have more economy, which supports playing larger creatures more consistently, although you won't be able to apply as much pressure as quickly as with Falcon Swarm or a Battle Forge rush.
I agree with most of what Silverclawgrizzly talked about, though I would add that Dissolve is also for Suppression Cloak.