A lead-acid battery that has sat for any period of time after complete discharge (more than a week) suffers from sulphation. Under normal operation, lead peroxide and lead are converted to lead sulphate while creating current flow. The lead sulphate mostly converts back to the original materials during the charge cycle. The small amount that doesn't is why lead acid batteries eventually fail.
When left set uncharged, lead sulphate converts to a more solid, crystalline state. The material produced is mostly incapable of being returned back to lead peroxide and lead.
You can play with pulse chargers on badly sulphated batteries, but it's mostly playing as you will never restore the battery to more than marginally useful capacity. The pulse charging also can cause material to spall off the plates, eventually shorting one of the cells.
Float charge or charge once a month to keep lead-acid batteries operational and prevent hard sulphation. In other words, once you've placed a UPS in operation, keep it plugged in on a power strip and let it power up for a day every couple of weeks during its 3-4 year battery life.
And if there are bulges, you have a shorted cell which is causing overcharge in the remaining cells. One or more cells are out of commission, the battery will never produce full power and probably won't run the UPS during power failure. Replace immediately or pull the battery, recycle it and mark the UPS as being out of commission till the battery is replaced.
NOTE: There are vendors out there that sell fully compatible batteries for a lot less than the original manufacturer sells them for. Most of the time, you will find they're the same exact battery model and manufacturer as the OEM battery.
If the battery replacement price isn't right, get a new UPS, the new one will be more efficient and the surge protection circuitry will be fresh and ready to protect your equipment than the old one anyway.